CAMBRIDGE    PHYSICAL    SERIES 


PHOTO-ELECTRICITY 


CAMBRIDGE    UNIVERSITY   PRESS 

fLonUon:    FETTER  LANE,   E.G. 

C.   F.  CLAY,  MANAGER 


OFUinburgf):   100,   PRINCES  STREET 

ILontJon:    H.    K.   LEWIS,   136,  GOWER  STREET,   W.C. 

ILontion:    WILLIAM  WESLEY  AND  SON,  28,  ESSEX  STREET,  STRAND 

Berlin:    A.  ASHER  AND  CO. 

ILetp^tg:    F.   A.   BROCKHAUS 

£eto  Soth:    G.   P.   PUTNAM'S  SONS 

Calcutta:    MACMILLAN  AND  CO.,   LTD. 
Toronto:    J.    M.   DENT  AND  SONS,   LTD. 

THE   MARUZEN-KABUSHIKI-KAISHA 


All  rights  reserved 


PHOTO-ELECTRICITY 


BY 


CSLS\j2_jz^y-^ 

ARTHUR   LLEWELYN   HUGHES,   D.Sc.,  B.A. 

ASSISTANT    PROFESSOR   OF    PHYSICS  \N    THE    RICE    INSTITUTE, 


HOUSTON,    TEXAS 


Cambridge : 
at  the  University   Pres 
1914     ^ 


Cambrtoge : 

PRINTED   BY  JOHN   CLAY,    M.A. 
AT   THE   UNIVERSITY   PRESS 


PREFACE 

SINCE  the  account  of  the  photo-electric  effect  given  by 
R.  Ladenburg  in  the  Jahrbuch  fur  Radioaktivitdt  for  1909, 
no  complete  resume  of  the  subject  has  been  written.  During 
the  past  five  years,  however,  considerable  progress  has  been  made, 
and  it  is  therefore  thought  desirable  to  give  some  account  of  the 
condition  of  the  subject  at  the  present  time.  Such  an  account  is 
attempted  in  this  book,  all  forms  of  ionisation  by  light  being 
considered,  whether  in  solids,  liquids  or  gases. 

The  photo-electric  effect  is  regarded  as  a  form  of  ionisation 
by  light  and  my  original  intention  was  to  use  the  latter  expression 
as  the  title  of  the  book.  But  this  title  suggests  perhaps  not  so 
much  the  study  of  the  emission  of  electricity  from  illuminated 
surfaces  among  other  phenomena,  as  a  study  merely  of  ionisation 
of  gases ;  and  as  most  of  our  information  as  to  ionisation  by  light 
has  been  obtained  from  a  study  of  the  photo-electric  effect  in 
solids  and  liquids,  it  was  thought  that  the  title  "Photo-Electricity" 
would  be  more  suggestive  of  the  contents  of  the  book. 

I  wish  to  express  rny  best  thanks  to  Mr  T.  G.  Bedford,  the 
Editor  of  the  Cambridge  Physical  Series,  for  many  valuable 
suggestions  and  for  help  in  the  revision  of  the  proofs. 

A.  LL.  HUGHES. 


HOPSTON,  TEXAS. 
October  1913. 


293532 


CONTENTS 


CHAP.  PAGE 

I.      INTRODUCTION 1 

II.       lONISATION  OF  GASES  AND  VAPOURS  BY  ITl/TRA-VlOLET  LlGHT  7 

Experimental  precautions.  Results  for  air  and  similar 
gases.  Effect  of  impurities.  Mobility  of  positive  ions. 
Results  for  chlorine  and  iodine.  Organic  vapours.  Metal- 
lic vapours. 

III.    THE  VELOCITIES  OP  EMISSION  OF  PHOTO-ELECTRONS    .        .          27 

Method  of  measuring  velocity.  Velocity  independent 
of  light  intensity.  Effect  of  frequency  and  nature  of 
metal  on  velocity.  Experimental  results.  Linear  relation 
between  maximum  emission  energy  and  frequency.  Quan- 
tum theory.  Richardson's  statistical  theory.  Resonance 
theories.  Ionising  potential  and  atomic  volume. 

IV.  THE  TOTAL  PHOTO-ELECTRIC  EFFECT 53 

Influence  of  gases.  lonisation  by  collision.  Photo- 
electric effect  and  light  intensity.  Photo-electric  effect 
and  temperature.  Photo-electric  effect  of  surfaces  treated 
by  an  electric  discharge.  Colloidal  modifications  of  the 
alkali  metals.  Photo-electric  fatigue.  Photo-electric  effect 
of  alloys. 

V.  THE  PHOTO-ELECTRIC  EFFECT  AS  A  FUNCTION  OF  THE  FRE- 

QUENCY AND  STATE  OF  POLARISATION  OF  THE  LIGHT    .          77 

Difference  between  alkali  metals  and  others.  Normal 
and  selective  effects.  Sensitiveness  of  new  surfaces. 

VI       PHOTO-ELECTRIC  PROPERTIES  OF  THIN  METALLIC  FILMS      .         92 

Asymmetric  emission  of  photo-electrons.  Electro- 
magnetic theory  and  asymmetry.  Peculiarities  in  photo- 
electric properties  of  thin  films. 

VII.     PHOTO-ELECTRIC  EFFECTS  OF  NON-METALLIC  ELEMENTS  AND 

INORGANIC  COMPOUNDS 100 

Elements.  Oxides.  Sulphides.  Salts.  Liquids.  In- 
sulators. 


Vlll  CONTENTS 

CHAP.  PAGE 

VIII.     PHOTO-ELECTRIC  EFFECTS  OF  DYES,  FLUORESCENT  AND  PHOS- 
PHORESCENT SUBSTANCES  .  119 


Dyes  in  aqueous  and  alcoholic  solutions.     Fluorescent 
solids.   Fluorescent  solutions.   Phosphorescent  substances. 


IX.  POSITIVE  RAYS  PRODUCED  BY  LIGHT 131 

X.  SOURCES  OF  LIGHT  USED  IN  PHOTO-ELECTRIC  EXPERIMENTS        134 

Mercury  lamp.  Sparks.  Discharge  in  hydrogen. 
Carbon  arc.  Transparency  of  fluorite,  quartz,  etc. 
Summary. 

NAME  INDEX    .        . 141 

SUBJECT  INDEX  143 


CHAPTER  I 

INTRODUCTION 

• 

THE  first  important  observation  on  the  action  of  light  on  the 
discharge  of  electricity  from  conductors  was  that  of  Hertz  in  1887, 
who  found  that  a  spark  passed  between  metallic  terminals  in  air 
more  easily  when  light  from  another  spark  fell  on  the  negative 
terminal.  This  effect  led  to  a  number  of  investigations  by 
Hallwachs,  Elster  and  Geitel,  and  others,  who  found  that  elec- 
trified metallic  conductors  lost  electrification  when  illuminated  by 
a  suitable  source  of  light.  On  taking  precautions  to  avoid  spurious 
effects,  the  important  result  was  established  that  the  illuminated 
metal  could  lose  negative,  but  not  positive  charges.  If  the  metal 
were  initially  insulated  and  uncharged,  then  it  acquired  a  small 
positive  charge  as  a  result  of  illumination,  but  the  potential  to 
which  it  rose  did  not  exceed  a  volt.  With  most  metals,  the  leak 
of  negative  electricity  ceased  on  the  interposition  of  a  plate  of 
glass  between  the  source  of  light  and  the  metal.  As  the  glass 
absorbs  the  ultra-violet  radiation,  it  was  thus  proved  that  the  effect 
in  these  metals  was  due  to  ultra-violet  light  alone. 

The  alkali  metals,  on  the  other  hand,  were  very  sensitive  to 
light  of  wave-lengths  within  the  range  of  the  visible  spectrum  as 
well  as  to  ultra-violet  light.  The  leak  of  negative  electricity  from 
an  illuminated  plate  occurred  whether  the  metal  was  surrounded 
by  a  gas  or  was  in  the  best  vacuum  obtainable,  but  the  rate  at 
which  the  leak  took  place  varied  considerably  with  the  nature 
and  pressure  of  the  surrounding  gas.  Investigations  were  made 
by  Stoletow  and  others  soon  after  the  discovery  of  the  effect  to 
determine  the  relations  between  the  leak  of  electricity  from  the 
illuminated  plate,  and  such  factors  as  the  pressure  of  the  gas  and 
the  electric  force  outside  the  illuminated  plate. 

H.  1 


•3 


[CHAP. 


The  emission  of  negative  electricity  from  an  illuminated  plate 
I  is  generally  known  as  the  photo-electric  effect,  or  sometimes  as 
I  the  Hallwachs  effect,  Hallwachs  being  one  of  the  first  to  in- 
jhvestigate  it.  No  satisfactory  explanation,  however,  of  the  loss  of 
flnegative  charge  by  a  metal  when  illuminated  was  given  until 
jithe  development  of  the  theory  of  the  ionisation  of  gases. 
v  Gases  in  their  ordinary  state  are  almost  perfect  insulators. 
The  simple  electroscope  shows  this  clearly.  When  the  rod  sup- 
porting the  gold  leaves  is  well  insulated,  the  gold  leaves  will 
retain  a  charge  for  days,  showing  that  the  air,  or  other  gas,  in  the 
electroscope  has  no  appreciable  conductivity.  If  now  a  flame,  or 
an  incandescent  solid,  be  brought  near  the  electroscope  so  that 
the  hot  gases  have  access  to  the  gold  leaves,  or  to  some  conductor 
in  metallic  connection  with  them,  the  leaves  will  immediately 
collapse,  showing  a  complete  loss  of  charge.  The  same  thing 
happens  if  a  beam  of  X-rays  is  directed  into  the  electroscope,  or 
if  some  radio-active  substance  is  placed  inside.  Suitable  control 
experiments  show  that  the  only  possible  explanation  is  that  the 
gas,  which  in  its  normal  state  is  an  insulator,  becomes  conducting 
under  the  influence  of  these  agents.  From  about  1896,  very 
rapid  progress  was  made  by  Sir  J:  J.  Thomson  and  his  pupils  in 
elucidating  the  nature  of  the  conductivity  imparted  to  gases  by 
various  agents,  and  particularly  by  X-rays.  The  X-rays  and  other 
ionising  agents  are  considered  to  produce  a  number  of  charged 
particles,  or  "ions,"  in  the  gas.  These  ions  are  molecules,  or 
small  aggregates  of  molecules,  which  differ  from  the  rest  in. 
possessing  electric  charges,  some  negative  and  some  positive.  In 
an  electric  field  they  move  towards  the  electrodes,  their  directions 
of  motion  depending  on  the  signs  of  their  charges.  On  arriving 
at  the  electrodes  the  ions  give  up  their  charges,  and  in  this  way 
the  discharging  effect  of  an  ionised  gas  is  explained. 

The  nature  of  ionisation  was  made  still  clearer  by  Sir  J.  J. 
Thomson's  discovery  of  the  existence  of  electrons,  which  are 
negatively  charged  particles  whose  masses  are  far  smaller  than 
•  those  of  atoms.  The  electron  is  now  regarded  as  the  ultimate 
unit  of  negative  electricity.  A  positive  charge,  on  the  other  hand, 
is  not  known  to  exist  as  a  separate  entity  apart  from  atoms  or 
molecules.  The  electrons  when  isolated  by  our  experimental 


l]  INTRODUCTION  3 

methods  are  always  moving  with  very  high  speeds,  from  107  to 
1010  cm. /sec.  The  fastest  electrons  may  collide  successively  with 
a  number  of  molecules,  and  the  effect  of  each  collision  is  to  reduce 
the  velocity  of  the  electron.  When  the  velocity  has  been  reduced 
to  about  108  cm./sec.,  the  electron  sticks  to  any  neutral  molecule 
or  atom  with  which  it  collides  and  forms  a  negative  ion.  Since 
ionisation  of  a  gas  by  X-rays  is  known  to  produce  equal  numbers 
of  positive  and  negative  ions,  it  is  natural  to  explain  the  negative 
ion  as  a  neutral  molecule  which  has  acquired  an  extra  electron, 
and  the  positive  ion  as  the  neutral  molecule  from  which  the 
electron  was  originally  emitted.  The  atom  on  the  electron  theory 
is  regarded  as  an  assemblage  of  electrons,  probably  in  rapid 
motion,  together  with  a  positive  nucleus,  so  that  the  atom  as  a 
whole  is  uncharged.  The  forces  keeping  the  electrons  in  position 
are  naturally  assumed  to  be  electrical.  When  sudden  and  violent 
changes  occur  in  the  atomic  forces  through  the  impact  of  a 
swiftly  moving  electron,  or  through  the  action  of  an  X-ray  pulse, 
or  ultra-violet  light,  the  atomic  system  may  be  so  much  disturbed 
that  one  of  the  electrons  leaves  the  system  altogether.  In  this 
way  one  pictures  the  phenomenon  of  ionisation.  When  ionisation 
is  confined  to  the  surface  layers  of  a  solid  or  liquid  substance, 
only  the  electron  can  escape  from  the  substance,  while  the 
positive  charge,  necessarily  associated  with  the  parent  atom, 
remains  in  the  surface.  In  the  presence  of  a  gas  these  electrons 
become  negative  ions.  The  electrons  or  negative  ions,  as  the 
case  may  be,  can  be  detected  experimentally  through  the  emission 
of  negative  electricity  from  the  surface,  provided  the  electric  field 
is  favourable.  It  is  a  characteristic  feature  of  surface  ionisation, 
however,  that  if  the  field  is  reversed  there  is  no  emission  of  positive 
electricity.  ^ 

The  experimental  evidence,  hitherto  considered,  indicates  that 
the  photo-electric  effect  is  localized  in  the  surface  of  the  metal, 
that  is  to  say,  ionisation  occurs  in  the  surface  itself — a  pheno- 
menon distinct  from  gaseous  ionisation  produced  by  X-rays.  This 
view  was  firmly  established  by  the  experiments  of  Sir  J.  J. 
Thomson1  and  Lenard2  who  found  that  a  metallic  plate  in  vacuo, 

1  Sir  J.  J.  Thomson,  Phil.  Mag.  XLVIII.  p.  547,  1899. 

2  Lenard,  Ann.  d.  Phys.  n.  p.  359,  1900. 

1—2 


4  PHOTO-ELECTRICITY  [CHAP. 

illuminated  by  ultra-violet  light,  emitted  electrons.  \  These  elec- 
trons have  velocities  of  the,  order  of  107  cm./sec.,  and  thus  are 
much  slower  than  ordinary  cathode  or  /3  rays.  It  is  convenient  to 
refer  to  the  electrons  emitted  from  illuminated  metals  as  photo- 
electrons,  thus  indicating  their  mode  of  production,  but  it  must 
not  be  taken  as  implying  that  they  are  in  any  way  different  from 
other  electrons.  This  discovery  of  the  emission  of  electrons  from 
illuminated  surfaces  made  it  possible  to  formulate  much  more 
definite  views  about  the  whole  subject  of  lonisation  by  light j 
The  primary  action  of  the  light  is  to  ionise  atoms  in  the  surface, 
that  is,  to  cause  them  to  emit  electrons,  some  of  which  get  away 
from  the  surface  and  can  be  detected  experimentally.  c, 

It  may  seem  somewhat  strange  that  ionisation  by  ultra-violet 
light  manifests  itself  as  a  surface  effect  in  solids  and  liquids,  while 
ionisation  by  almost  all  other  agents  appears  most  evident  in 
gases.  Yet  there  is  no  fundamental  distinction  on  this  account. 
Ultra-violet  light — provided  extremely  short  wave-lengths  are  used 
— does  ionise  gases  just  as  readily  as  X-rays.  But  with  the 
ordinary  sources  of  ultra-violet  light,  the  surface  effect  is  the 
only  one  observed,  and  the  methods  ,of  investigating  it  differ 
considerably  from  the  methods  employed  in  studying  gaseous 
ionisation. 

.  With  the  progress  of  experimental  knowledge,  it  has  become 
clearer  that  each  substance  has  a  definite  wave-length  at  which  its 
photo-electric  effect  starts.  Wave-lengths  longer  than  this  are 
incapable  of  causing  the  emission  of  photo-electrons,  while  all 
wave-lengths  shorter  than  this  are  effective.  The  critical  wave- 
lengths for  the  alkali  metals  are  in  the  visible  spectrum,  for  the 
other  metals  they  are  between  X2500  and  X4000,  and  for  the  non- 
metals  they  lie  beyond  X2200,  the  wave-lengths  being  measured 
in  Angstrom  units  (10~8  cm.).  The  critical  wave-length  for  oxygen 
is  about  XI 350.  There  is  considerable  experimental  difficulty  in 
working  with  such  short  wave-lengths,  and  this  has  seriously 
hampered  the  study  of  ionisation  of  gases  by  ultra-violet  light. 
In  general,  the  more  electro-positive  an  element  is,  the  longer  is 
i  the  wave-length  at  which  the  ionisation  begins.  The  critical 
wave-length  at  which  the  photo-electric  effect  starts  has  recently 
acquired  an  important  significance,  for  on  certain  theories  we  can 


I]  INTRODUCTION  5 

immediately  calculate  from  it  the  work  that  is  necessary  to  take 
an  electron  away  from  its  parent  atom.  This  is  a  quantity  of 
fundamental  importance  in  the  electrical  theory  of  atomic  struc- 
ture, for  it  measures  the  potential  energy  between  the  electron  in 
its  equilibrium  position  and  the  rest  of  the  atomic  system.  For 
this  reason  I  have  endeavoured  to  indicate,  wherever  possible, 
the  wave-length  at  which  the  photo-electric  effect  starts  for  the 
substance  investigated.  Unfortunately  there  is  often  much  un- 
certainty in  arriving  at  a  correct  estimate,  since  many  experi- 
menters have  approached  the  subject  from  quite  a  different  point 
of  view,  and  explicit  information  as  to  the  effective  spectral 
region  is  wanting.  We  may  almost  say  that  the  critical  wave- 
length at  which  the  photo-electric  effect  starts  completely  charac- 
terizes the  photo-electric  behaviour  of  a  substance  so  far  as  the 
fundamental  process  is  concerned.  Of  course,  the  actual  experi- 
mental photo-electric  currents  are  influenced  by  a  number  of 
secondary  effects  such  as  the  absorption  of  the  active  light  and  of 
the  electrons  by  matter. 

The  photo-electric  effect  was  among  the  first  phenomena  toi 
receive  an  interpretation  on  the  quantum  theory  of  radiation.! 
The  characteristic  feature  of  the  quantum  theory  is  that  the 
transference  of  energy  to  or  from  the  radiant  form  is  not  con- 
tinuous, but  takes  place  in  small  finite  units.  ^An  unexplained 
peculiarity  of  the  theory  is  the  necessary  assumption  of  the 
variation  of  the  unit  of  energy  from  one  wave-length  to  another.) 
The  unit  of  energy  is  directly  proportional  to  the  frequency  of 
the  radiant  energy,  and  is  therefore  equal  to  hn,  where  n  is  the 
frequency  and  h  a  constant  known  as  "Pfl.np.lj>  constant.  Hence  if 
the  energy  is  completely  transferred  to  the  photo-electron  when 
light  ionises  a  molecule,  the  energy  of  the  photo-electron  should 
be  proportional  to  the  frequency  of  the  light.  Experiments 
have  now  shown  quite  definitely  that  this  is  the  case.  When  the 
quantum  theory  was  first  applied  to  the  photo-electric  effect  it 
was  assumed  that  the  light  was  molecular  in  structure,  each 
"molecule"  or  unit  containing  an  amount  of  energy  hn  which 
could  not  be  subdivided,  and  therefore  on  interaction  with  matter 
was  wholly  transferred  to  the  photo-electron.  Although  many 
experiments  show  a  remarkable  agreement  with  the  predictions 


6  PHOTO-ELECTKICITY  [CHAP.    I 

of  the  quantum  theory,  it  is  such  a  radical  departure  from  the 
classical  views  of  the  nature  of  radiant  energy  that  many  attempts 
have  been  made  to  explain  the  results  on  lines  more  in  accordance 
with  the  older  ideas.  The  view  now  prevalent  is  that  the  quantum 
theory  gives  the  correct  mathematical  expression  for  the  energy 
transformations,  but  gives  no  indication  of  the  nature  of  the 
phenomena  to  which  it  is  applied. 

In  discussing  photo-electric  experiments,  it  is  often  desirable 
to  know  what  part  of  the  spectrum  produced  the  effect  under 
consideration.  As  most  investigators  do  not  give  any  informa- 
tion on  this  point,  beyond  merely' stating  their  source  of  light, 
it  was  thought  that  a  short  account  of  the  various  sources  of 
light  used  in  photo-electric  experiments  would  be  useful.  This 
will  be  found  in  Chapter  x,  together  with  some  observations  on  the 
regions  of  the  spectrum  of  the  light  transmitted  by  a  number  of 
substances  including  quartz  and  fluorite. 


CHAPTEK  II 

IONISATION    OF   GASES   AND    VAPOURS    BY 
ULTRA-VIOLET   LIGHT 

THE  interpretation  of  experiments  on  gases  is  always  much 
simpler  than  the  interpretation  of  experiments  on  solids  and 
liquids.  This  is  due  to  the  comparatively  simple  conception  of 
the  physical  state  of  a  gas  which  we  have  in  the  kinetic  theory 
of  gases.  Not  only  is  our  picture  of  the  molecular  state  of  a 
solid  or  liquid  much  less  defined  and  precise,  but  also  the  difficulty 
of  interpreting  our  results  is  considerably  increased  by  the 
necessity  for  taking  intermolecular  forces  into  account  in  any 
explanation  which  aims  at  completeness.  A  considerable  amount 
of  positive  knowledge  has  been  acquired  as  to  the  nature  of 
ionisation  by  Rontgen  rays,  and  much  of  this  is  due  to  the  fact 
that  the  effect  can  be  studied,  with  comparative  ease,  in  gases. 
-Thus  we  know  indirectly  from  ionisation  experiments,  and  more 
recently  directly  from  C.  T.  R.  Wilson's  experiments,  that 
ionisation  by  Rontgen  rays  consists,  first  of  the  expulsion  of  a 
number  of  corpuscles  moving  with  high  speeds  from  certain  mole- 
cules, and  secondly,  of  the  ionisation  of  a  much  larger  number  of 
molecules  by  these  corpuscles.  But  when  we  turn  to  ionisation 
by  light,  almost  all  the  experiments  have  been  concerned  with 
the  photo-electric  effect  at  solid  or  liquid  surfaces.  The  difficulties 
of  interpreting  such  experiments  with  any  degree  of  exactness 
has  doubtless  caused  investigators  from  time  to  time  to  turn  to 
the  ionisation  of  gases  by  light.  Unfortunately  it  has  been 
extremely  difficult  to  get  any  evidence  of  true  ionisation  of  gases 
by  light  until  comparatively  recently,  to  say  nothing  of  a^ detailed 
investigation  of  the  phenomenon.  The  experimental  difficulties 
are  such  that  almost  all  the  experiments  are  restricted  to  proving 


8 


PHOTO-ELECTRICITY 


[CHAP. 


that  the  ionisation  exists,  or  does  not  exist,  under   certain  con- 
ditions of  illumination. 

A  general  consideration  of  the  photo-electric  effect  leads  to 
the  conclusion  that  the  more  electronegative  an  element,  the  more 
difficult  it  is  to  ionise  it  by  light.  In  more  precise  terms,  this 
means  that  the  longest  wave-length  which  is  capable  of  ionising 
an  element  goes  more  and  more  into  the  ultra-violet  as  the 
element  becomes  more  and  more  electronegative,  All  the  gases 
and  vapours  which  are  convenient  to  use  in  ionisation  experiments 
are  electronegative,  and  it  so  happens  that  the  wave-lengths 
which  are  effective  in  such  gases  can  only  be  got  experimentally 
with  special  precautions.  For  example,  only  specially  selected 
specimens  of  clear  fluorite  will  transmit  the  light  which  ionises 
air ;  all  other  solid  substances  are  opaque  to  the  light. 

.A  few  remarks  on  the  peculiar  difficulties  met  with  in  investi- 
gating ionisation  by  light  should  be  useful  at   this  point.     As 

to  potential 


quartz 


I - 


Mo  earth 
to  electroscope 

Fig.  1. 


ionisation  chambers  usually  have  electrodes  made  of  some  metal 
or  other  conductor,  spurious  results  are  frequently  obtained  due 
to  photo-electric  action  at  the  electrodes  which  give  relatively  big 
effects.  The  following  is  an  example  of  spurious  results  of  this 
kind  obtained  on  one  occasion  and  illustrates  the  care  which  must 
be  taken  in  these  experiments.  An  ionisation  chamber  of  the  form 
shown  in  Fig.  1  was  made  so  that  no  light  fell  directly  on  the 
electrode  E.  The  light  passed  in  through  a  quartz  window  from 
a  discharge  in  hydrogen.  It  is  now  known  that  this  light  is 
incapable  of  ionising  air.  Yet  in  this  apparatus  a  small  leak  of 
the  order  10~15  amp.  was  always  obtained.  .  Now  it  was  found  that 
when  the  same  light  fell  upon  a  surface  of  the  same  nature  as  the 
inside  (lamp-black  surfaces)  of  the  ionisation  vessel,  a  leak  of 


II]  IONISATION   BY   ULTRA-VIOLET   LIGHT  9 

10~10  amp.  was  obtained.  The  first  leak  of  10~15  amp.  might  be 
accounted  for  by  a  trace  of  light  finding  its  way  to  the  electrode 
after  several  reflections.  An  amount  only  10~5  of  the  incident 
light  would  be  sufficient,  and  it  is  difficult  to  be  certain  that  this 
is  not  the  true  explanation  of  the  leak.  A  decisive  test  was  the 
following.  A  surface  effect  would  decrease  continuously  as  the 
pressure  of  the  gas  increased  (assuming  no  ionisation  by  collision). 
A  volume  effect  on  the  other  hand  would,  at  some  stage  or  other, 
increase  with  the  pressure.  As  the  leak  decreased  with  increasing 
pressure,  it  was  concluded  that  the  small  effect  obtained  was 
merely  a  surface  effect  at  the  electrode. 

Perhaps  the  best  method  of  testing  for  ionisation  by  light 
is  to  illuminate  a  stream  of  gas  and  then  to  pass  it  through  an 
ionisation  chamber  where  the  conductivity  can  be  tested.  If 
proper  precautions  are  taken  to  prevent  the  entry  of  any  light 
into  the  ionisation  chamber,  the  presence  of  positive  ions  as  well 
as  negative  ions  in  the  stream  of  gas  can  be  taken  as  conclusive 
evidence  of  the  ionisation  of  the  gas.  Further  tests  must  be  made 
to  determine  whether  the  gas,  or  some  impurity  in  it,  is  ionised, 
but  at  all  events  the  effect  is  not  due  to  a  spurious  surface  effect. 
The  presence  of  negative  ions  alone  simply  points  to  a  photo- 
electric effect  at  the  surfaces  on  which  the  light  falls,  in  the 
neighbourhood  of  the  window.  The  disadvantage  of  this  method 
is  that  very  large  quantities  of  gas  are  required  to  sweep  through 
the  apparatus  and  the  difficulties  of  ensuring  a  large  supply  of 
pure  gas  are  considerable.  This  is  the  method  which  has  been 
adopted  by  practically  all  investigators  on  ionisation  of  gases  by 
light. 

Experimental  Results  for  Air  and  similar  Gases. 

The  earliest  experiments  of  any  importance  on  ionisation  of 
gases  by  light  were  those  made  by  Lenard1.  The  light  was 
obtained  from  an  intense  spark  between  metallic  terminals.  Air 
illuminated  by  this  light  was  found  to  discharge  both  positively 
and  negatively  charged  bodies,  hence  ions  of  both  signs  must  have 
been  present  in  the  air.  Most  of  the  experiments  were  carried  out 
with  the  unfiltered  air  of  the  room,  though  some  experiments 
1  Lenard,  Ann.  d.  Phys.  i.  p.  486,  1900;  HI.  p.  298,  1900. 


10  PHOTO-ELECTRICITY  [CHAP. 

were  made  on  dust-free  gases.  lonisation  of  the  same  order  was 
obtained  in  air,  carbon  dioxide  and  oxygen,  a  smaller  effect  in  coal 
gas  and  a  very  small  effect  in  hydrogen.  The  ionising  light  was 
found  to  be  strongly  absorbed  by  air,  carbon  dioxide  and  oxygen, 
and  more  strongly  still  by  coal  gas.  In  the  case  of  the  filtered 
gases,  appreciable  effects  were  only  obtained  when  the  spark  was 
within  a  few  mm.  of  the  quartz  window.  /^This  indicates  that  the 
ionising  light  is  located  far  in  the  ultra-violet.  One  peculiar  result 
was  that  the  ionisation  was  more  powerful  in  fresh  air  than  in  air 
which  had  been  illuminated  for  some  time.  Again,  the  mobilities 
of  the  ions  produced  in  unfiltered  air  were  measured  and  found  to 
be  3'13cm./sec.  for  the  negative  ion  and  -0015cm./sec.for  the  positive 
ion — the  latter  being  of  quite  a  different  order  from  the  mobility  of 
the  positive  ion  produced  by  Rontgen  rays,  etc.  These  two  observa- 
tions point  very  strongly  to  the  explanation  that  the  conductivity 
observed  is  due  to  the  presence  of  dust  particles,  or  other  nuclei, 
which  emit  electrons  like  ordinary  surfaces  when  illuminated  and 
remain  positively  charged.  Their  low  mobility  is  explained  by  their 
great  mass  relative  to  that  of  the  molecules  and  the  fatigue-like 
effect  is  due  to  the  removal  of  the  positively  charged  particles  by 
the  electric  field.  Mobility  experiments  were  not  made  with  the 
filtered  gases,  hence  it  is  not  certain  that  the  conductivity  of  the 
gases  indicates  that  an  ionisation  of  the  gases  themselves  takes 
place,  since  ultra-violet  light  may  produce  in  filtered  gases  nuclei 
which  are  photo-electric  (p.  19). 

Bloch1  showed  that  the  ionisation  obtained  by  Lenard  was 
really  due  to  a  photo-electric  effect  of  the  minute  dust  particles 
suspended  in  the  air.  On  filtering  the  air,  the  number  of  positive 
ions  produced  was  reduced  to  zero.  It  should  be  mentioned 
however  that  in  a  few  experiments  of  Lenard  the  light  had  to 
traverse  shorter  distances  than  in  Bloch's,  and  so  Bloch's  con- 
clusions are  not  strictly  applicable  to  these.  However,  when  the 
light  has  to  traverse  5  cm.  of  air  or  more  and  a  quartz  plate, 
Bloch's  experiments  show  that  filtered  air  is  not  ionised. 

The  method  of  studying  ionisation  by  means  of  condensa- 
tion nuclei  as  developed  by  C.  T.  R.  Wilson2  is  the  most  sensitive 

1  Bloch,  Le  Radium,  p.  240,  1908. 

2  C.  T.  E.  Wilson,  Phil.  Trans.  A.  cxcu.  p.  403,  1899. 


II]  IONISATION    BY   ULTRA-VIOLET   LIGHT  11 

method  known  for  detecting  small  amounts  of  ionisation.  When 
the  air  in  the  expansion  apparatus  was  illuminated  by  Rontgen 
rays,  large  numbers  of  charged  nuclei  were  produced.  But  while 
ultra-violet  light  also  produced  nuclei,  they  differed  from  the 
other  nuclei  in  that  they  were  uncharged.  Wilson  concludes  that 
the  nuclei  produced  by  ultra-violet  light  are  chemical  products  due 
to  illumination  of  the  air  saturated  with  water  vapour.  When  the 
ultra-violet  light  was  very  intense,  clouds  were  formed  with  very 
small  expansions  or  even  without  any  expansion  and  lasted  for  a 
long  time.  Wilson  points  out  that  the  drops  cannot  be  pure  water; 
he  suggests  that  hydrogen  peroxide  is  formed  which,  when  dissolved 
in  the  water  drops,  alters  the  vapour  pressure  so  that  the  drops 
remain  in  permanent  equilibrium.  Any  real  effect,  which  would 
be  shown  by  the  presence  of  charged  nuclei,  is  masked  in  these 
experiments  by  the  presence  of  vast  numbers  of  uncharged  nuclei 
which  are  produced  photo-chemically.  Wilson  used  a  quartz 
window  and  the  distance  of  the  spark  from  it  varied  from  a  few 
cm.  upwards.  Hence  the  light  probably  did  not  contain  wave- 
lengths shorter  than  XI 770.  It  seems  unfortunate  that  such  an 
extraordinarily  sensitive  method  for  detecting  ionisation  should, 
in  this  particular  case,  be  rendered  useless  by  the  production  of 
photo-chemical  nuclei  which  mask  any  real  ionisation  effect. 
Since  these  nuclei  are  produced  by  the  interaction  of  water  and 
oxygen,  a  way  out  of  the  difficulty  would  be  to  use  some  organic 
liquid,  which  did  not  give  rise  to  photo-chemical  nuclei,  instead  of 
water. 

Sir  J.  J.  Thomson1  found  that  the  light  from  a  lime  cathode 
discharge,  after  passing  through  a  quartz  window  '3  mm.  thick, 
produced  a  very  small  conductivity  in  a  stream  of  gas  passing  the 
window.  The  natural  conductivity  in  air  was  increased  8  times, 
in  carbon  dioxide  60  times,  and  in  ammonia  150  times.  The 
spectrum  of  the  lime  cathode  discharge  has  probably  never  been 
investigated  in  the  Schumann  region  (Chap,  x),  but  we  may  take 
it  that  wave-lengths  shorter  than  X1450  are  absent.  From  later 
experiments  described  below,  it  is  concluded  that  pure  air  is  not 
ionised  by  light  of  wave-lengths  longer  than  XI 350.  With  shorter 
wave-lengths  very  large  ionisations  were  obtained.  Possibly  these 
1  Sir  J.  J.  Thomson,  Proc.  Camb.  Phil.  Soc.  xiv.  p.  417,  1908. 


12 


PHOTO-ELECTRICITY 


[CHAP. 


experiments  with  the  lime  cathode  discharge  indicate  that  thin 
quartz  transmits  traces  of  light  of  the  necessary  short  wave-lengths, 
but  in  far  too  attenuated  an  amount  to  be  detected  by  the  spectro- 
scopic  method.  It  is  much  more  likely,  however,  that  the  very 
small  effect  obtained  for  air  was  due  to  the  traces  of  impurities 
which,  according  to  Lenard,  are  very  difficult  to  get  rid  of,  and 
which  account  for  the  conductivity  in  air  when  illuminated  by 
the  light  passed  through  a  quartz  plate. 

In  1910  the  author1  investigated  the  ionisation  of  air  by  ultra- 
violet light.  The  apparatus  used  is  shown  in  Fig.  2.  The  source 
of  light  was  a  discharge  in  hydrogen  at  a  pressure  of  about  1  mm. 
The  filtered  air  streams  up  against  the  window  F  and  then  passes 


\*~  hydrogen  discharge  tube 


2nd  electroscope 


Fig.  2. 

into  the  chamber  G  in  which  the  conductivity  is  tested.  Par- 
ticular care  was  taken  to  prevent  any  light  (except  possibly  after 
three  reflections)  from  entering  the  testing  chamber,  which  was 
of  brass,  and  therefore  photo-electrically  active.  The  criterion 
for  gaseous  ionisation,  as  distinct  from  a  mere  surface  effect,  is 
the  presence  of  positive  as  well  as  negative  ions  in  the  gas  after 
illumination.  When  the  window  F  was  of  quartz  '3  mm.  thick, 
no  positive  ions  could  be  detected,  though  the  apparatus  was 
sensitive  enough  to  detect  a  current  of  the  order  of  10~15  amp. 
On  substituting  a  certain  plate  of  fluorite  for  the  quartz,  an 
enormous  number  of  positive  ions  was  obtained,  the  leak  now  being 
of  the  order  of  10~~n  amp.  The  following  control  experiments 
1  Hughes,  Proc.  Camb.  Phil.  Soc.  xv.  p.  483,  1910. 


Il]  IONISATION    BY    ULTRA-VIOLET   LIGHT  13 

were  made.  There  was  no  leak  (1)  when  the  air  was  illumi- 
nated but  at  rest,  and  (2)  when  the  air  was  in  motion  but  not 
illuminated.  The  absence  of  nuclei  which  might  emit  photo- 
electrons  as  a  surface  effect  when  illuminated  was  confirmed  by 
drawing  the  illuminated  air  from  the  testing  chamber  into  a  Wilson 
expansion  apparatus.  No  drops  or  clouds  were  formed  when  the 
expansion  was  less  than  1'25,  showing  the  absence  of  nuclei  larger 
than  the  ordinary  ions. 

It  was  desirable  to  find  the  wave-length  of  the  light  which 
produced  the  ionisation  in  air.  From  the  experimental  relations 
discussed  in  the  next  chapter  we  can  find  the  shortest  wave-length 
transmitted  through  a  substance  by  measuring  the  maximum 
emission  velocity  of  photo-electrons  from  a  suitable  surface 
illuminated  by  light  passing  through  the  substance.  Several 
plates  of  quartz  (*3  mm.  thick)  gave  practically  identical  emission 
velocities ;  hence  their  transparency  limits  are  the  same.  Accord- 
ing to  Lyman,  the  transparency  limit  of  such  plates  of  quartz  is 
X1450.  On  the  other  hand,  the  transparency  limits  of  different 
pieces  of  clear  fluorite  were  found  to  vary  enormously.  The  only 
piece  of  fluorite  which  transmitted  light  capable  of  ionising  air 
was  unfortunately  broken  before  its  transparency  limit  could  be 
ascertained.  The  most  transparent  of  the  other  pieces  of  fluorite 
which  did  not  transmit  the  ionising  light  was  opaque  to  light  of 
wave-lengths  less  than  X1350.  We  may  therefore  conclude  that 
air  is  not  ionised  appreciably  by  light  of  wave-lengths  greater 
than  X1350.  It  is  unlikely  that  the  best  fluorite  plate  which  was 
used  transmitted  light  of  shorter  wave-lengths  than  Lyman's  best 
specimens,  and  hence  we  may  conclude  from  these  experiments 
that  the  intense  ionisation  of  air  by  ultra-violet  light  begins  at 
some  wave-length  which  is  between  XI 250  and  \1350,  and  mostj 
probably  nearer  to  the  latter  limit. 

Some  experiments  were  made  on  the  mobilities  of  the  positive 
ions  produced  in  air  by  ultra-violet  light,  as  Lenard's  early  experi- 
ments suggested  that  the  positive  ion  produced  by  ultra-violet 
light  was  much  heavier  than  that  produced  by  other  ionising 
agents.  The  apparatus  shown  in  Fig.  2  was  again  used.  Along  the 
axis  of  the  brass  cylinder  C  there  are  two  electrodes  connected  to 
tilted  electroscopes.  When  the  potential  of  the  cylinder  differs  from 


14 


PHOTO-ELECTRICITY 


[CHAP, 


that  of  the  electrodes,  a  radial  electric  field  is  established.  In 
addition  to  having  the  same  velocity  as  the  gas  parallel  to  the 
axis,  the  ions  possess  a  radial  velocity  depending  on  the  electric 
field  and  the  mobilities  of  the  ions.  Hence,  when  the  ionised  air 
flows  through  the  apparatus  at  a  constant  rate,  the  ratio  of  the 
charges  received  by  the  two  electrodes  is  a  function  of  the 
potential  of  the  outer  cylinder  and  the  mobility  of  the  ions.  The 
ratio  of  the  charge  received  by  the  second  electrode  to  the 
total  charge  received  by  the  two  will  give  the  proportion  of 
the  ions  driven  to  the  second  electrode,  and  if  we  plot  the 


24  uolts 


Fig.  3. 


ratio  of  the  charges  against  the  potentials  of  the  outer  cylinder, 
when  the  stream  of  air  is  ionised  alternately  by  Rontgen  rays 
and  ultra-violet  light,  the  curves  will  coincide  if  the  mobilities 
of  the  ions  are  identical.  The  ionisation  by  Rontgen  rays  was 
limited  to  a  layer  about  '5  cm.  thick  just  below  the  fluorite 
window,  so  that  the  distribution  of  the  ions  in  the  stream  of  air 
would  be  practically  the  same  as  when  the  air  was  ionised  by 
ultra-violet  light.  Fig.  3  shows  that  the  mobility  of  the  positive 
ion  is  the  same  whether  it  is  produced  by  Rontgen  rays  or  by 
ultra-violet  light.  Hence  so  far  as  mobility  is  a  criterion,  the 


Il]  IONISATION   BY   ULTRA-VIOLET  LIGHT  15 

positive  ion  produced  by  ultra-violet  light  is  indistinguishable 
from  that  produced  by  Rontgen  rays.  Such  a  result  naturally 
follows  if  we  regard  the  positive  ion  as  a  molecule  deprived  of  an 
electron  by  light  in  the  one  case  and  by  the  impact  of  a  swiftly 
moving  corpuscle  in  the  other.  There  was  no  evidence  of  any 
positive  ions  possessing  very  small  mobilities  in  these  experiments. 
Palmer1  investigated  the  ionisation  produced  by  ultra-violet 
light  of  short  wave-length  in  a  number  of  gases,  viz.  air,  hydrogen, 
oxygen  and  nitrogen.  The  apparatus  was  identical  in  principle 
with  that  described  above.  A  novel  feature  was  the  introduction 
of  a  small  absorption  cell  1  cm.  long,  bounded  by  fluorite  windows, 
between  the  hydrogen  discharge  tube  and  the  illuminated  cham- 
ber through  which  the  gas  passed  on  its  way  to  the  testing 
apparatus.  The  absorption  cell  could  be  filled  with  oxygen  at 
any  desired  pressure  so  as  to  alter  the  nature  of  the  ionising 
light.  Lyman's  experiments  showed  that  a  fluorite  cell  containing 
oxygen  transmits  light  belonging  to  the  following  spectral  regions. 

Pressure  of  02  Region  transmitted 

0  XI 250  to  the  visible  spectrum 

15  mm.  X 1250  to  X 1350  and  X  1500         „  „  „ 

40  mm.  X  1250  to  X  1330  and  X  1600         „  „  „ 

760mm.  X  1250  to  X  1270  and  XI 760 

In  Fig.  4  the  current  is  plotted  against  the  pressure  of  oxygen 
in  the  absorption  cell2.  Equal  numbers  of  positive  and  negative 
ions  were  obtained,  the  greatest  leak  being  of  the  order  10~n  amp. 
We  see  that  the  ionisation  decreases  rapidly  as  the  range  of 
wave-lengths  transmitted  in  the  neighbourhood  of  \  1300  becomes 
smaller.  When  there  is  no  oxygen  in  the  absorption  cell,  the 
number  of  ions  produced  in  air  is  intermediate  between  that 
produced  in  oxygen  and  in  nitrogen.  When  some  of  the  light  is 
cut  out  by  the  oxygen  in  the  absorption  cell,  this  no  longer  holds. 
Before  we  can  interpret  the  results  exactly,  we  should  know 
whether  the  ionising  light  is  completely  absorbed  in  the  stream  of 
gas  (1  cm.  thick)  and  whether  any  recombination  takes  place 
on  the  way  to  the  testing  chamber.  It  is  remarkable  that  the 

1  Palmer,  Phys.  Rev.  xxxn.  p.  1,  1911. 

2  I  am  indebted  to  Professor  Palmer  for  the  footnote  to  the  curves  which  was 
omitted  in  the  original  paper  through  a  printer's  mistake. 


16 


PHOTO-ELECTRICITY 


[CHAP. 


ionisation  in  nitrogen  should  be  so  much  greater  than  that  in 
oxygen  when  we  consider  that  oxygen  absorbs  light  in  this  region 
of  the  spectrum  much  more  strongly  than  nitrogen. 

Palmer  obtained  a  very  small  ionisation  in  hydrogen  when 
the  absorption  cell  was  empty.  Since  the  method  of  experiment 
requires  large  quantities  of  gas,  it  is  difficult  to  be  certain  that 
the  gas  is  absolutely  pure  and  consequently  some  slight  impurity 
may  be  responsible  for  the  effect.  Lyman  found  (spectroscopically) 
no  trace  of  absorption  of  the  Schumann  region  by  hydrogen, 
and  ionisation  cannot  take  place  without  absorption.  It  must 


25 


15 


10 


20 


60 


so  cm 


40 

Pressure 
Fig.  4. 

A,  ionisation  in  nitrogen, 

B,  „  oxygen, 

C,  „  air. 

be  remembered,  however,  that  ionisation  tests   are   much   more 
sensitive  than  absorption  tests. 

Palmer  concludes  that  the  ionisation  of  air  by  light  begins  with 
wave-lengths  shorter  than  A,  1850.  We  think  the  evidence  is  in 
favour  of  displacing  the  limit  much  further  into  the  ultra-violet. 
Even  when  the  absorption  cell  was  full  of  oxygen,  some  light  of 
wave-lengths  near  A,  1250  was  transmitted  and  the  ionisation  might 


II]  IONISATION   BY    ULTRA-VIOLET    LIGHT  17 

be  due  to  this.  A  decisive  test  for  the  existence  of  ionisation  with 
wave-lengths  greater  than  X  1500  could  be  made  by  using  thin 
quartz  instead  of  fluorite,  but  Palmer  did  not  investigate  this  point. 

Cannegieter1  investigated  whether  the  light  due  to  an  electrical 
discharge  through  a  gas  was  specially  effective  in  producing  ion- 
isation in  the  same  gas,  but  concluded  that  such  was  not  the  case. 
The  result  that  the  ionisation  is  of  the  same  order  in  hydrogen, 
nitrogen,  carbon  dioxide  and  air  is  quite  opposed  to  all  other 
researches  on  the  subject  and  may  possibly  be  accounted  for  by 
surface  effects. 

Lenard  and  Ramsauer2  have  made  an  elaborate  series  of 
experiments  on  the  ionisation  of  gases  by  ultra-violet  light  and 
other  problems  arising  therefrom.  The  source  of  light  was  a 
very  intense  spark  between  aluminium  terminals,  produced  by  a 
large  induction  coil  which  could  take  90  amperes  in  the  primary. 
The  spark  gap  was  in  parallel  with  a  condenser  whose  capacity 
was  about  :I  microfarad.  With  such  a  source  of  ultra-violet  light, 
the  intensity  of  ionisation  in  air  was  greater  than  has  ever  been 
obtained  in  cold  gases  except  Avhen  cathode  rays  transmitted 
through  a  thin  aluminium  window  were  used.  Part  of  the 
ionisation  is  attributed  to  a  comparatively  penetrating  ultra- 
violet light  whose  wave-length  is  conjectured  to  be  about  X  900. 
The  authors  investigated  very  thoroughly  the  role  played  by 
the  suspended  nuclei  and  gaseous  impurities  in  the  experiments 
on  ionisation  by  light.  The  effect  of  such  impurities  is  to  mask,  in 
an  extraordinary  manner,  the  real  ionisation  effects  in  air.  Among 
the  gaseous  impurities  which  give  misleading  effects  are  carbon 
dioxide  and  ammonia.  Both  these  are  ionised  by  the  quartz-violet. 
(Quartz-violet  and  fluorite-violet  are  convenient  terms  introduced 
by  the  authors  and  require  no  explanation.)  Other  impurities 
which  give  large  effects  are  the  vapours  occluded  on  glass  surfaces, 
in  glass  and  cotton-wool  and  in  rubber  tubes.  The  compressed 
gases  in  cylinders  contain  some  impurities  which  increase  the 
ionisation  due  to  ultra-violet  light  many  times. 

1  Cannegieter,  DIM.,  Utrecht,  1911;  Ber.  d.  Akad.  d.  Wissensch.  Amsterdam, 
p.  1114,  1911. 

2  Lenard  and  Ramsauer,   Sitzungsberichte  d.   Heidelberger  Akad.  d.  Wisscn. 
1910—1911. 

H.  2 


18  PHOTO-ELECTRICITY  [CHAP. 

The  authors  found  that  it  was  necessary  to  purify  the  air 
by  freezing  out  impurities  in  liquid  air  and  to  get  rid  of  the 
occluded  vapours  by  heating  strongly  all  the  glass  tubing  of  their 
apparatus.  It  was  only  when  this  was  done  that  spurious  effects 
were  avoided.  Air  purified  in  this  way  could  only  be  ionised  by 
the  light  which  passed  from  the  spark  through  a  fluorite  plate. 
When  a  quartz  plate  was  substituted  for  the  fluorite  plate,  the 
ionisation  did  not  take  place.  The  fluorite-violet  produced  an 
effect  5'7  times  as  great  in  carbon  dioxide  as  .in  air.  The  quartz- 
violet  produced  an  appreciable  effect  in  carbon  dioxide  in  addition. 
(Sir  J.  J.  Thomson  (loc.  cit.)  also  found  that  carbon  dioxide  and 
ammonia  were  ionised  by  the  quartz- violet.)  The  effect  in 
hydrogen,  purified  by  freezing  out  impurities  by  liquid  air,  was 
about  equal  to  that  in  air.  The  hydrogen  was  from  a  cylinder  and 
possibly  contained  air  which  may  have  accounted  for  the  effect. 

Traces  of  ammonia  and  carbon  disulphide  in  air  were  found  to 
increase  the  ionisation  due  to  the  fluorite-violet  44  and  14  times 
respectively.  It  may  be  mentioned  here  that  similar  results  were 
obtained  by  Palmer1  when  the  air  contained  traces  of  alcohol  and 
ether.  It  is  noteworthy  that  small  quantities  of  water  vapour  in 
air  did  not  produce  any  effect  in  the  quartz-violet.  In  the  fluorite- 
violet  the  presence  of  water  vapour  reduces  the  effect.  The 
water  vapour  was  found  to  produce  considerable  absorption  in 
the  light  which  ionised  air.  Hence  when  water  vapour  takes  part 
in  absorption  as  well  as  air,  less  ionisation  is  produced  and  one 
may  conclude  from  these  experiments  that  water  vapour  is  less 
ionised  (if  at  all)  than  air  by  the  fluorite-violet. 

Lenard  and  Ramsauer  made  experiments  on  the  mobility  of 
the  ions  and  found  that,  under  different  conditions,  ions  varying 
much  in  size  could  be  produced  by  ultra-violet  light.  Their  con- 
clusions may  be  summarized  as  follows.  The  ions  are  originally 
of  molecular  size,  which  indicates  that  they  originate  in  much 
the  same  way  as  other  ions.  From  experiments  on  the  growth 
of  the  ions  it  was  concluded  that  the  very  big  ions  were  not 
produced  by  accumulation  of  molecules  round  a  charged  ion. 
The  molecular  ions  do  not  grow  to  any  extent  in  this  way.  The 
big  ions  are  formed  when  solid  or  liquid  particles  (condensation 
1  Palmer,  Phys.  Eev.  xxxn.  p.  1,  1911. 


II]  IONISATION  BY  ULTRA-VIOLET  LIGHT  19 

nuclei)  are  suspended  in  the  gas.  The  nuclei  may  be  produced 
by  the  light  itself.  The  small  ions  may  collide  with  and  stick 
to  these  big  nuclei  forming  a  heavy  ion.  There  is  no  evidence 
that  the  heavy  ions  are  built  up  by  repeated  additions  to  the 
charged  nucleus.  Condensation  nuclei  are  produced  in  air  by 
light  unless  it  is  carefully  purified  from  condensable  impurities  \ 
by  cooling.  Solid  nuclei  of  ammonium  nitrate  and  nitrite  appear 
to  be  formed  when  air  containing  traces  of  ammonia  is  illuminated 
by  light  of  short  wave-length.  These  nuclei  can  grow  to  a  very 
large  size.  Hydrogen  peroxide  nuclei  are  also  produced.  Their 
size  depends  on  the  degree  of  saturation  of  water  vapour  present. 
So  far  as  is  known  at  present,  chemical  changes  are  not  accom- 
panied by  ionisation. 

Bloch1  has  verified  the  ionisation  of  air  by  Schumann  rays. 
He  also  found  that  air  could  be  ionised  by  the  light  from  a 
mercury  lamp.  As  the  shortest  wave-length  available  was  prob- 
ably X  1849,  it  seems  likely  that  the  effect  observed  was  due  to 
traces  of  impurities.  It  is  not  recorded  whether  he  went  to  the 
same  trouble  as  Lenard  and  Ramsauer  did  to  remove  these  im- 
purities. Bloch's  arrangement  enabled  all  the  light  emitted  to 
be  available  for  ionisation  and  hence  the  impurities  had  every 
chance  to  affect  the  results. 

Discussion  of  Results  for  Air. 

We  shall  now  consider  the  experimental  results  given  above 
and  try  to  form  some  estimate  of  the  longest  wave-length  which 
will  ionise  air.  By  air  is  meant  the  usual  mixture  of  oxygen  and 
nitrogen  free  from  all  other  more  condensable  gases.  One  fact  which 
is  quite  evident,  is  that  in  all  the  experiments  in  which  abundant 
ionisation  of  pure  air  has  been  obtained,  fluorite  has  been  used 
instead  of  thin  quartz.  The  hydrogen  discharge  used  by  Hughes 
and  by  Palmer  is  exceedingly  rich  in  wave-lengths  between  \  1300 
and  \  1600  according  to  Lyman's  investigations.  Hence  with  thin 
quartz,  very  intense  light  with  wave-lengths  between  X 1450  and 
X  1600  is  available.  No  one  has  succeeded  in  showing  that  the 
light  emitted  by  a  hydrogen  discharge  and  passed  through  quartz 

1  Bloch,  Comptes  Rendus,  pp.  903,  1076,  1912. 

2—2 


20  PHOTO-ELECTRICITY  [CHAP. 

produces  any  appreciable  Honisation  in  air.  In  the  experiments  of 
the  author,  thin  quartz  and  a  piece  of  fluorite  which  only  trans- 
mitted light  of  wave-length  longer  than  X  1350  did  not  produce 
any  measurable  ionisation  in  air,  while  another  piece  of  fluorite 
which  could  hardly  have  transmitted  light  of  shorter  wave-length 
than  X1250,  enabled  an  effect  to  be  obtained  103  or  104  times  as- 
great  as  the  least  effect  which  could  be  detected.  In  Palmer's 
;;xperime»ts,  the  fluorite  absorption  cell,  filled  with  oxygen,  always 
allowed  some  light  in  the  neighbourhood  of  X  1260  to  pass,  so  we 
cannot  draw  any  certain  conclusions  from  his  work  as  to  the  problem 
in  hand.  It  is  significant  that  Lenard  and  Ramsauer  did  not  obtain 
any  ionisation  in  pure  air  with  light  which  passed  through  quartz, 
though  their  source,  being  a  very  powerful  one,  was  particularly 
well  adapted  to  make  any  small  effect  evident.  According  to 
Lyman,  the  spectrum  of  the  aluminium  spark  in  air  shows  strong 
lines  near  X  1300,  weak  lines  near  X  1500,  and  strong  lines  near 
X  1600  and  X  1720  to  X  1800.  Thin  quartz  cuts  out  the  X  1300 
group.  The  X  1500  and  X  1600  groups  may  possibly  have  been 
ineffective  in  Lenard  and  Ramsauer 's  work  owing  to  absorption 
by  air  outside  the  window,  as  they  do  not  explicitly  state  that 
they  ever  put  the  spark  close  up  to  the  window  when  using  quartz 
as  they  did  when  using  fluorite. 

From  analogy  with  photo-electric  experiments  on  metals,  it 
seems  likely  that  the  ionisation  of  a  gas  sets,  in  at  some  definite 
wave-length  and  increases  with  great  rapidity  with  decreasing 
wave-length,  and  hence  this  critical  wave-length  should  be  fairly 
well  defined.  If  we  assume  that  the  quantum  theory  is  applicable 
to  the  problem  in  hand,  we  can  calculate  what  the  critical  wave- 
length should  be  (p.  43).  If  V0e  is  the  energy  required  to  take  an 
electron  from  a  molecule,  and  if  the  electron  is  absorbing  energy  from 
light  whose  frequency  is  n,  then  the  energy  in  the  quantum,  hn, 
must  exceed  V$e  in  order  that  ionisation  should  be  possible.  Taking 
h  =  6'55  x  10~27  erg  sec.,  e  =  4*65  x  1 0~10  E.S.U.,  and  the  critical 
wave-length  to  be  X  1350,  we  get  for  F0  the  value  9'2  volts. 
Ionisation  can  be  produced  by  the  impact  of  an  electron  on  a 
molecule.  Before  the  electron  can  produce  ionisation,  its  kinetic 
energy  must  exceed  the  energy  required  to  ionise  a  molecule. 
Ve  is  the  energy  acquired  by  an  electron  moving  freely  between 


II ]  ION1SATION   BY   ULTRA-VIOLET   LIGHT  21 

two  points  whose  potential  difference  is  V.  When  Ve  is  equal 
to  the  energy  required  to  ionise  a  molecule,  V  is  called  the  ionising 
potential.  The  most  accurate  measurements  of  the  ionising  poten- 
tials are  those  of  Franck  and  Hertz1,  who  give  9'0  volts  for  oxygen. 
(For  nitrogen  they  give  7'5  volts  and,  working  backwards,  this 
indicates  that  ionisation  in  nitrogen  should  be  possible  with  about 
a  wave  Jength  of  \  1620.  However,  before  we  get  ionisation,  we 
must  have  absorption  and  the  absorption*  by  nitrogen  is  scarcely 
observable  until  we  get  to  shorter  wave-lengths.  A  smaller  ionising 
potential  for  nitrogen  than  for  oxygen  was  hardly  to  be  expected 
from  indirect  estimates  based  on  ionisation  by-collision.)  Our  con- 
clusion that  \  1350  is  the  critical  wave-length  for  oxygen  is  there- 
fore in  good  agreement  with  theoretical  deductions.  A  considerably 
larger  value  for  the  critical  wave-length,  such  as  \  1800,  would 
be  inconsistent  with  the  indications  of  the  quantum  theory.  In 
viewr  of  the  wide  application  of  the  quantum  theory  to  molecular 
physics  and  especially  the  simple  explanation  which  it  affords 
of  the  photo-electric  effect,  the  experimental  evidence  does  not 
seem  strong  enough  to  warrant  our  rejecting  X 1350  as  the  critical 
wave-length  for  air  in  favour  of  a  considerably  longer  wave-length. 

Chlorine  and  Iodine. 

Ludlam2  -found  that  the  fluorite- violet  did  not  produce  any 
ionisation  in  pure  chlorine  although  marked  effects  were  obtained 
with  the  same  light  in  air.  That  the  long  wave-length  limit 
should  be  shorter  for  chlorine  than  for  air  is  to  be  expected,  as  it 
is  one  of  the  most  strongly  electronegative  elements  known. 

The  ionisation  of  iodine  vapour  has  been  sought  by  several 
investigators  on  account  of  the  fluorescence  which  is  produced  in 
it  by  light  of  comparatively  long  wave-lengths. 

Henry3  and  Whiddington4,  both  using  the  light  from  a  carbon 
arc  transmitted  through  quartz,  could  not  find  any  ionisation. 
Franck  and  Westphal5  confirmed  these  results,  but  most  of  the 
ultra-violet  light  was  cut  out  by  the  glass  of  their  apparatus. 

1  Franck  and  Hertz,  Verh.  d.  Deutsch.  Phys.  Ges.  xv.  p.  34,  1913. 

2  Ludlam,  Phil.  Mag.  xxin.  p.  757,  1912. 

3  Henry,  Proc.  Camb.  Phil  Soe.  ix.  p.  319,  1898. 

4  Whiddington,  Proc.  Camb.  Phil.  Soc.  xv.  p.  189,  1910. 

5  Franck  and  Westphal,  Verh.  d.  Deutsch.  Phys.  Ges.  xiv.  p.  159,  1912. 


22  PHOTO-ELECTRICITY  [CHAP. 

They  obtained  the  very  interesting  result  that,  while  fluorescing 
iodine  vapour  was  not  ionised  itself,  it  was  easier  to  produce  a 
glow  discharge  through  the  fluorescing  iodine  vapour  than  through 
the  non-fluorescing  vapour.  Apparently,  less  work  is  required  to 
separate  an  electron  from  a  molecule  when  it  fluoresces  than  when 
it  does  not. 

It  would  have  been  interesting  to  investigate  the  ionisation 
in  iodine  vapour  by  the  fluorite-violet.  Being  less  electronegative 
than  chlorine,  ionisation  might  possibly  be  obtained. 

Organic   Vapours. 

Stark1  investigated  the  conductivity  of  a  number  of  organic 
vapours  when  illuminated  by  ultra-violet  light.  He  obtained 
decisive  evidence  of  ionisation  in  anthracene,  diphenylmethane,  a- 
naphthylamine,  and  diphenylamine.  The  light  used  was  that  from 
a  mercury  lamp,  which  was  not  likely  to  emit  wave-lengths  shorter 
than  X1849.  The  compounds  were  introduced  into  a  highly  ex- 
hausted quartz  tube  (about  3  cm.  wide)  provided  with  nickel- 
steel  electrodes.  The  vapour  pressure  was  varied  by  altering  the 
temperature  of  the  tube.  At  low  temperatures,  when  the  vapour 
pressure  is  quite  negligible,  the  leak  obtained  on  illumination 
must  be  due  to  the  photo-electric  effect  at  the  electrodes.  Pro- 
vided ionisation  by  collision  is  avoided,  this  leak  should  decrease 
as  the  pressure  of  the  vapour  is  increased,  owing  to  absorption. 
But  if  ionisation  occurs  in  the  vapour  itself,  it  will  increase  as  the 
pressure  increases  until  there  is  complete  absorption  of  the  ionising 
light.  Beyond  this,  the  leak  should  remain  constant  or  decrease. 
In  Fig.  5  the  current  through  the  illuminated  tube  is  plotted 
against  the  pressure.  The  current  due  to  the  surface  effect  would 
be  represented  by  some  such  curve  as  a,  and  that  due  to  the 
ionisation  of  the  vapour  by  b,  while  their  sum  represented  by 
the  curve  c  is  that  which  is  actually  observed  experimentally. 
One  can  only  conclude  definitely  that  there  is  ionisation  in  the 
vapour  itself  when  the  leak,  at  some  stage  or  other,  increases  with 
the  pressure.  The  following  are  the  results  obtained  with  anthra- 
cene and  they  are  also  typical  of  the  results  for  the  other  sub- 
stances. It  will  be  observed  that  the  ionisation  current  is  quite  a 
big  one,  in  fact  big  enough  to  allow  a  galvanometer  to  be  used. 

1  Stark,  Phijs.  Zeits.  x.  p.  614,  1909. 


IONISATION   BY   ULTRA-VIOLET  LIGHT 


23 


The  mercury  lamp  was  placed  close  to  the  tube  containing  the 
anthracene. 

Current  due  to 
illumination 

Lowest  pressure  (temp.  -70°C.)  100  x  10 -10  amp. 

As  pressure  increases,  leak  falls  to  10  „ 

„  „  then  rises  to  a  max.  50  „ 

„  „  and  finally  decreases  to  1  „ 

As  the  field  never  exceeded  4  volts  per  cm.,  the  increase  in  the 
current  with  the  pressure  cannot  be  attributed  to  ionisation  by 
collision.  The  pressure  at  which  the  maximum  ionisation  took 
place  was  estimated  to  be  40 — 50  mm.  On  measuring  the  leak 
corresponding  to  different  voltages,  it  was  found  that  the  leak 
increased  almost  linearly  up  to  12  volts  (the  maximum  tried). 


Current 


Pressure 


Fig.  5. 


The  current  corresponding  to  this  was  1'2  x  10~8  amp.  and  the 
12  volts  meant  a  field  of  about  5  volts  per  cm.  Stark  concluded 
from  this  that  recombination  was  greater  when  the  ionisation  was 
produced  by  light  than  when  it  was  produced  by  Rontgen  rays,  etc. 
The  electrons  have  only  a  small  velocity  of  separation  and  conse- 
quently they  fall  back  into  the  parent  molecule  much  more  easily 
than  if  they  had  been  electrons  of  high  speed  produced  by  Rontgen 
rays.  In  view  of  our  later  knowledge  concerning  ionisation  by 
Rontgen  rays,  particularly  from  C.  T.  R.  Wilson's  experiments, 
Stark's  explanation  is  by  no  means  so  attractive  as  it  appeared  at 
first  sight.  High  speed  corpuscles  are  produced  by  Rontgen  rays, 
but  their  separation  from  their  parent  molecules  is  not  the  pheno- 
menon of  ionisation.  Each  high  speed  corpuscle  in  passing 
through  the  gas  causes  the  ionisation  of  many  molecules  and  this 


24  PHOTO-ELECTRICITY  [CHAP 

process  consists  in  the  separation  of  electrons  from  molecules  with 
velocities  of  the  same  order  as  those  of  photo-electrons.  It  seems 
probable  that,  with  the  same  density  of  ionisation  and  the  same 
fields,  any  other  ionising  agent  would  have  given  currents  far  from 
saturation.  A  test  of  this  kind  does  not  appear  to  have  been  made. 
These  vapours  all  show  intense  fluorescence  when  suitably 
illuminated.  Stark  developed  a  theory  in  which  the  fluorescence 
was  identified  with  disturbances  of  the  valency  electron  of  the 
carbon  atom  of  the  condensed  benzol  ring.  He  considered  that 
the  ionisation  and  fluorescence  were  closely  connected  and  therefore 
concluded  that  the  same  electron  was  involved  in  both  effects. 

Serkof,  working  in  the  Cavendish  Laboratory,  investigated  the 
ionisation  in  a  large  number  of  organic  vapours  by  Stark's  method, 
improved  in  certain  respects.  The  source  of  light  was  a  mercury 
lamp.  He  obtained  evidence  of  ionisation  in  only  one  vapour, 
viz.  aniline,  in  addition  to  those  .which  Stark  found  to  be  ionised. 
It  is  interesting  to  note  that  the  aniline  vapour  had  (compared 
with  the  other  vapours)  a  large  conductivity  in  the  dark.  It  may 
be  pointed  out  that  the  five  vapours,  in  which  Stark  and  Serkof 
obtained  ionisation  by  the  light  from  a  mercury  lamp,  all  contain 
the  condensed  benzol  ring. 

The  writer1  investigated  the  effect  of  ultra-violet  light  on  a 
number  of  vapours.  The  vapours  chosen  were  carbon  disulphide 
(CS2),  zinc  ethyl  (Zn  (C2H5)2)  and  tin  tetrachloride  (Sn014),  each  of 
which  contains  one  element  at  least  which  has  marked  photo-electric 
properties.  The  light  from  a  mercury  lamp  was  used  as  the  source 
and  therefore  the  shortest  wave-length  available  was  X1849.  Not 
a  trace  of  ionisation  was  observed  in  any  of  the  vapours,  while  they 
all  absorbed  the  ultra-violet  light  powerfully.  In  the  case  of  the 
zinc  ethyl,  the  light  which  when  totally  absorbed  in  it  did  not 
produce  any  ionisation  current  greater  than  10~15  amp.,  produced 
a  photo-electric  leak  from  a  zinc  plate  of  the  order  106  x  10~15  amp. 
It  may  be  concluded  therefore  that  light  of  wave-length  longer 
than  XI 849  is  incapable  of  causing  the  emission  of  an  electron 
from  a  molecule  of  these  vapours.  Analogous  results  were  ob- 
tained when  investigating  the  photo-electric  effects  of  certain  salts 
(Chap.  vil).  In  the  case  of  some  salts  however,  it  was  observed 
that  the  light,  while  not  producing  a  photo-electric  effect,  caused 
1  Hughes,  Proc.  Camb.  Phil  Soc.  xvi.  p.  375,  1911. 


Il]  IONISATION   BY   ULTRA-VIOLET  LIGHT  25 

a  decomposition  of  the  salt.  A  similar  effect  with  these  vapours 
was  not  looked  for  directly,  but  no  striking  evidence  of  such  de- 
composition was  noticed. 

Metallic  Vapours. 

Steubing1  employed  Stark's  method  to  show  that  mercury 
vapour  could  be  ionised  by  the  light  from  a  mercury  lamp.  The 
current  obtained  through  the  tube  when  the  pressure  of  mercury 
vapour  was  zero  was  10~8  amp.  This  was  the  photo-electric  effect 
at  the  electrodes.  On  increasing  the  vapour  pressure  of  the 
mercury  by  heating,  the  current  rose  to  a  maximum  value  of 
6  x  10~8  amp.  The  current  was  found  to  increase  almost  linearly 
with  the  potential  difference  up  to  12  volts  (the  maximum  em- 
ployed) and  it  was  suggested  that  Stark's  explanation  of  the 
similar  effect  in  the  organic  vapours  applied  also  to  the  ionisation 
of  mercury  vapour  by  light.  Steubing2  points  out  that  all  the 
vapours  in  which  he  and  Stark  obtained  ionisation  have  high 
molecular  weights.  v' 

The  only  other  experiments  on  the  ionisation  of  metallic 
vapours  are  those  of  Anderson3  on  potassium  vapour.  Experiments 
on  the  vapours  of  the  alkali  metals  present  many  difficulties  and 
the  results  are  somewhat  difficult  to  interpret.  Anderson  used 
visible  light  and  caused  his  apparatus  to  go  through  a  cycle  of 
temperature  changes.  He  found  that  the  leak  due  to  illumination, 
which  increased  with  rise  of  temperature  and  therefore  with  the 
density  of  the  vapour,  did  not  diminish  again  with  fall  of  tempera- 
ture. This  suggests  that  the  effect  observed  was  really  due  to  a 
photo-electric  effect  at  a  thin  imperceptible  layer  of  potassium 
which  was  condensed  on  the  electrodes,  and  not  to  a  real  ionisation 
of  the  vapour.  It  would  be  very  useful  for  theoretical  purposes  to 
know  whether  the  photo-electric  effect  sets  in  at  the  same  wave- 
length for  a  substance  in  the  gaseous  state  as  in  the  solid  state.  It 
seems  quite  possible  that  the  proximity  and  consequent  interaction 
of  the  molecules,  in  the  latter  state,  would  enable  an  electron  to 
be  detached  more  easily  from  a  molecule  than  when  the  molecule 
is  isolated  as  in  a  gas. 

1  Steubing,  Phys.  Zeits.  x.  p.  787,  1909. 

2  Steubing,  Jahrbuch  d.  Radioaktivitat,  April  1912. 

3  Anderson,  Phys.  Rev.  (2)  i.  p.  233,  1913. 


26  PHOTO-ELECTRICITY  [CHAP.   II 

Summary. 

Almost  all  the  experiments  on  ionisation  of  gases  by  ultra- 
violet light  have  been  concerned  merely  with  establishing  the 
existence  of  ionisation  in  gases  and  vapours  under  certain  con- 
ditions. Our  knowledge  from  such  experiments  of  the  nature  and 
mechanism  of  ionisation  by  light  does  not  extend  beyond  the  fact 
that  light  produces  ions  in  air  of  the, same  mobility  as  those  pro- 
duced by  Rontgen  rays.  Up  to  the  present,  the  experimental 
difficulties  have  prevented  any  detailed  investigation  of  the  way 
in  which  the  ionisation  depends  upon  the  various  factors  in  the 
problem.  For  example,  it  is  almost  impossible  to  study  the  ionisa- 
tion of  the  permanent  gases  by  monochromatic  light  as  no  apparatus 
is  available  which  will  isolate  light  of  wave-lengths  less  than  XI 850. 
Longer  wave-lengths  may  suffice  for  some  vapours,  but  the  necessity 
for  maintaining  these  vapours  at  high  temperatures  introduces 
considerable  experimental  difficulties.  The  following  are  among 
the  questions  which  remain  unanswered.  How  does  the  number 
of  ions  produced  in  a  gas  by  unit  energy  of  light  vary  with  the 
wave-length  ?  Does  this  variation  depend  on  the  nature  of  the 
gas  ?  How  much  of  the  energy  of  the  ionising  light  appears  as 
energy  of  ionisation  ?  How  does  the  ionisation  depend  on  the 
temperature,  pressure,  and  mixture  of  gases  ?  Experiments  on 
metallic  vapours  which  may  be  ionised  by  light  of  sufficiently  long 
wave-lengths  are  most  likely  to  give  the  desired  information.  The 
answers  to  some  of  these  questions  are  suggested,  but  only  in- 
definitely, by  investigations  of  the  photo-electric  effect  of  solids — 
metals  in  particular.  There  is  always  a  good  deal  of  uncertainty 
in  the  interpretation  of  experiments  on  solids.  The  number  of 
electrons  emitted  by  a  solid  surface  when  illuminated  by  light  is 
a  function  of  (1)  the  depth  to  which  the  light  penetrates,  (2)  the 
velocity  of  the  electrons  released,  since  this  determines  the  thick- 
ness of  the  layer  from  which  the  electrons  can  emerge,  and  (3)  the 
physical  state  of  the  surface  layers,  including  presence  of  occluded 
gases,  incipient  oxidation,  etc.  In  so  far  as  these  effects  cannot 
be  taken  into  consideration  quantitatively,  the  results  of  photo- 
electric experiments  on  solids  are  difficult  to  interpret  with 
precision. 


CHAPTER  III 

THE   VELOCITIES    OF    EMISSION    OF   PHOTO-ELECTRONS 

AN  accurate  knowledge  of  the  velocities  with  which  photo- 
electrons  emerge  from  illuminated  surfaces  is  of  great  importance 
in  the  discussion  of  the  photo-electric  effect.  At  the  present  time, 
the  test  afforded  by  our  experimental  knowledge  of  the  velocities 
of  photo-electrons  is  more  conclusive  and  better  adapted  for 
discriminating  between  theories  of  ionisation  by  light  than  any 
other  experimental  evidence  we  possess  in  this  branch  of  physics. 

An  illuminated  plate  emits  photo-electrons  with  velocities 
ranging  from  a  maximum  velocity  down  to  zero.  We  are  chiefly 
concerned  with  the  maximum  emission  velocity;  the  smaller 
velocities  are  probably  due  to  loss  of  energy  by  the  photo-electrons 
in  passing  molecules  in  the  surface  layers.  The  velocities  of  photo- 
electrons  are  almost  invariably  found  from  the  potential  difference 
which  will  bring  them  to  rest.  When  an  illuminated  plate  is  at 
a  positive  potential  with  respect  to  the  surrounding  electrode,  the 
electric  force  reduces  the  velocity  of  a  photo-electron  travelling 
away  from  the  plate.  If  the  potential  difference  is  such  that  the 
gain  of  potential  energy  by  an  electron  in  moving  from  the  plate 
to  the  surrounding  electrode  slightly  exceeds  its  initial  kinetic 
energy,  the  electron  is  brought  to  rest  just  before  it  reaches  the 
surrounding  electrode  and  then  returns  to  the  plate  under  the 
action  of  the  electric  force.  Thus  if  we  illuminate  an  insulated 
plate,  initially  at  the  same  potential  as  the  surrounding  electrode, 
photo-electrons  will  leave  it  and  its  (positive)  potential  will  increase 
until  the  kinetic  energy  of  the  fastest  photo-electron  is  just  in- 
sufficient to  enable  it  to  pass  from  the  plate  to  the  surrounding 
electrode.  When  this  stage  is  reached,  the  potential  of  the  plate 
does  not  increase  any  further.  If  V  be  the  final  potential  difference, 


28  PHOTO-ELECTRICITY  [CHAP. 

then  the  potential  energy  gained  by  an  electron  in  passing  from 
the  plate  to  the  electrode  is  Ve.  Since  this  must  equal  the  initial 
kinetic  energy  of  the  fastest  photo-electron,  we  have 

imv*=Ve  (1), 

where  e/m  =1*75  x  107  E.M.u. 

This  method  of  measuring  the  velocity  of  a  photo-electron  has  led 
to  the  somewhat  undesirable  practice  of  referring  to  the  velocity 
of  an  electron  as  a  velocity  of  so  many  volts.  The  actual  velocity 
in  cm./sec.  can  always  be  found  from  the  formula.  Thus  when  an 
electron  is  said  to  have  a  "  velocity  of  1  volt,"  its  real  velocity  is 
5'9  x  107  cm./sec.  The  actual  velocity  is  proportional  to  the  square 
root  of  the  voltage. 

The  study  of  the  emission  velocities  of  photo-electrons  resolves 
itself  into  an  investigation  of  the  relations  between  the  velocities 
and  (a)  the  intensity  of  the  light,  (6)  its  frequency  and  (c)  the 
nature  of  the  illuminated  surface. 

Effect  of  the  Intensity  of  the  Light  on  the  Velocities 
of  Emission. 

Lenard1  first  established  the  important  result  that  the  velocities 
of  photo-electrons  are  independent  of  the  intensity  of  the  light  pro- 
ducing them.  This  is  of  the  greatest  importance  for  it  shows  that 
the  magnitude  of  the  electric  force  in  the  beam  of  light  does  not 
determine  the  emission  velocity.  This  result  has  since  been  verified 
by  Ladenburg2,  Millikan  and  Winchester3,  Mohlin4  and  Elster  and 
Geitel5.  A  very  convincing  verification  of  the  fact  is  afforded  by  the 
recent  experiments  of  Millikan  in  which  the  emission  velocities  of 
photo-electrons  from  a  plate,  illuminated  by  light  of  the  same  wave- 
length from  a  mercury  arc  and  from  an  electric  spark,  were  found 
to  be  identical.  This  was  only  established  after  the  most  rigorous 
precautions  had  been  taken  to  exclude  electric  waves  by  completely 
enclosing  the  velocity  measuring  apparatus  in  a  metal  box.  For 
some  time  it  was  thought  that  the  spark  produced  photo-electrons 

1  Lenard,  Ann.  d.  Phys.  vm.  p.  149,  1902. 

2  Ladenburg,  Verh.  d.  Deutsch.  Phys.  Ges.  ix.  p.  504,  1907. 

3  Millikan  and  Winchester,  Phil.  Mag.  xiv.  p.  188,  1907. 

4  Mohlin,  Akad.  Abhandl.,  Upsala,  1907. 

5  Elster  and  Geitel,  Phys.  Zeits.  ix.  p.  451,  1908. 


Ill]       THE   VELOCITIES   OF  EMISSION   OF   PHOTO-ELECTRONS  29 

of  higher  velocity  than  the  arc,  but  now  these  experiments  must 
be  regarded  as  still  another  striking  illustration  of  the  extreme 
difficulty  of  shielding  off  electric  waves.  Provided  that  adequate 
precautions  are  taken  to  shield  the  velocity  measuring  apparatus 
from  electric  waves,  the  velocities  produced  by  the  same  wave- 
lengths from  the  arc  and  from  the  spark  are  identical  (Millikan1, 
Pohl  and  Pringsheim2).  Taking  the  mean  intensity  of  the  spark 
and  arc  to  be  of  the  same  order,  it  is  evident  that  the  actual 
intensity  of  the  spark  during  the  short  periods  of  illumination 
(separated  by  long  periods  of  rest)  is  very  much  greater  than  that 
of  the  arc.  Hence  the  identity  of  the  velocities  (for  the  same 
wave-length),  when  the  plate  is  illuminated  by  the  arc  and  spark 
in  turn,  proves  that  the  emission  velocities  are  quite  independent 
of  the  intensity  of  the  light. 

The  remarkably  high  values  sometimes  obtained  for  the  velocities 
when  electric  sparks  are  used  as  sources  of  light  arise  in  this  way. 
The  spark  emits  light  and  electric  waves  simultaneously.  When  the 
waves  pass  over  the  velocity  measuring  apparatus,  the  momentary 
potential  difference  between  the  illuminated  plate  and  the  sur- 
rounding electrode  is  by  no  means  the  steady  potential  difference 
given  by  the  voltmeter.  Hence  the  apparent  potential  difference 
as  observed  does  not  give  us  any  idea  of  the  effective  potential 
difference  at  the  instant  of  illumination  and  conclusions  drawn 
from  the  apparent  potentials  are  quite  incorrect. 

^Effect  of  the  Frequency  of  the  Light  and  the  Nature  of  the 
illuminated  Metal  on  the  Velocities  of  Emission. 

The  velocities  of  photo-electrons  are  known  to  depend  on  two] 
factors,  the^frequency^pf  the  Jight,  used,  and  the  nature  of  the! 
illuminated  metal.  Early  experiments  showed  that  the  shorter 
the  wave-length  of  the  light  used  for  illuminating  the  metal,  the 
greater  were  the  velocities  of  emission  of  the  electrons.  In  order 
to  discriminate  between  theories  of  the  photo-electric  effect,  it  is 
necessary  to  know  the  mathematical  form  of  the  relation  between 
the  velocity  and  the  frequency.  Two  laws  have  been  put  forward 
to  represent  the  experimental  results. 

1  Millikan,  Phys.  Eev.  i.  p.  73,  1913. 

2  Pobl  and  Pringsheim,  Verh.  d.  Deutsch.  Phys.  Ges.  xv.  p.  974,  1912. 


30  PHOTO-ELECTRICITY  [CHAP. 

(1)  According  to  one  law,  the  maximum  emission  velocity  of 
a  photo-electron  is  a  linear  function  of  the  frequency.  Expressed 
in  symbols,  this  is 


where  n  is  the  frequency,  k'  and  c  are  constants  and  V  is  the 
potential  difference  required  to  bring  the  fastest  photo-electron  to 
rest.  By  equation  (1),  p.  28,  VF  is  proportional  to  its  velocity. 
We  shall  refer  to  this  law  as  the  "  velocity  law."  When  simplified 
by  the  omission  of  the  constant  c,  it  is  sometimes  known  as 
Ladenburg's  law. 

(2)  The  other  law  is  that  the  maximum  emission  energy  of  a 
photo-electron  is  a  linear  function  of  the  frequency,  and  is  repre- 

sented by 

V  =  kn-V0   ...........................  (2). 

V  has  the  same  meaning  as  before  and  is  therefore  proportional  to 
the  energy  of  the  photo-electron,  k  and  V0  are  constants.  We 
shall  refer  to  this  law  as  the  '(energy  law.') 

For  a  considerable  period,  the  experimental  results  were  not 
sufficiently  accurate  to  decide  between  the  two  laws.  The  recent 
investigations  of  the  author  and  of  Richardson  and  Compton  show, 
however,  that  the  relation  between  the  velocity  and  frequency  is 
in  good  agreement  with  the  energy  law  but  riot  with  the  velocity 
law. 

The  relation  between  the  velocity  of  the  photo-electrons 
emitted  from  different  metals  and  the  frequency  of  the  light  is 
always  found  to  be  represented  by  equation  (2),  but  the  value  of 
the  constant  F0  depends  on  the  nature  of  the  metal. 

Equation  (2)  when  put  in  the  form 

Ve  —  ke.  n  —  F0  e, 

in  which  the  terms  are  of  the  dimensions  of  energy,  suggests  that 
ke  .  n  is,  in  some  way  or  other,  the  amount  of  energy  which  the 
photo-electron  has  to  begin  with  and  that  Vfie  may  be  looked  upon 
as  the  sum  of  the  energy  lost  in  escaping  from  the  parent  atom  and 
the  energy  lost  in  passing  through  the  surface  layer.  If  we  assume 
that  the  latter  does  not  exist  when  the  metallic  surfaces  are  pre- 
pared by  distillation  in  vacuo,  then  V0e  may  be  regarded  in  this 
case  as  the  work  spent  in  escaping  from  the  atom.>ic 


Ill]        THE  VELOCITIES  OF   EMISSION  OF   PHOTO-ELECTRONS  31 

Distribution  of  Energy  among  the  Photo- Electrons. 

The  current  from  the  illuminated  plate  is  often  measured  as  a, 
function  of  the  potential  difference  between  the  plate  and  the 
surrounding  electrode.  The  results  are  usually  given  in  curves 
of  which  Fig.  6  is  typical. 

Accelerating  potential  denotes  that  the  potential  difference  is 
in  such  a  direction  as  to  assist  the  escape  of  the  photo-electrons. 
A  retarding  potential  AO  is  just  sufficient  to  stop  all  the  electrons 
and  therefore  measures  thve  maximum  emission  energy.  Bb  repre- 
sents the  number  of  electrons  possessing  velocities  greater  than 
that  corresponding  to  Ob  (volts).  With  accelerating  potentials 


Retarding     '  Accelerating 

Potential  Potential 

Fig.  6. 

greater  than  Od,  the  photo-electric  current  is  constant.  It  is 
evident  that  we  can  deduce  from  the  curve  the  number  of  electrons 
possessing  any  given  velocity.  For  this  reason,  such  curves  have 
frequently  been  termed  "  velocity  distribution  curves."  This  term 
is  however  not  strictly  correct,  for  the  curves  do  not  actually  give 
a  direct  relation  between  the  velocity  and  number.  The  part  CD 
apparently  indicates  that  a  certain  number  emerge  only  when 
assisted  by  a  small  accelerating  field.  A  variety  of  causes  may 
contribute  to  this  effect. 

(1)  Reflection  of  electrons.  Some  of  the  electrons  leaving  the 
illuminated  plate  may  be  reflected  back  again  from  the  surrounding 
electrode.  This  return  of  electrons  is  prevented  when  the  ac- 
celerating potential  exceeds  Od. 


32 


PHOTO-ELECTRICITY 


[CHAP. 


(2)  Poor  vacuum.     If  the  electrons  stick  to  molecules,  then 
those  molecules  which  happen  to  be  travelling  towards  the  illumi- 
nated electrode  bring  the  charge  back  again.     This  effect  is  only 
prevented  by  an  appreciable  accelerating  field. 

(3)  Stray  magnetic  fields  of  a  few  gausses.     An  electron  of 
velocity  corresponding  to  1  volt  would,  in  the  absence  of  an  electric 
field,  describe  a  circle  of  radius  3'5  cm.  in  a  field  of  1  gauss  applied 
at  right  angles  to  its  direction  of  motion.     If  the  apparatus  is  big 
enough  to  contain  such  an  orbit,  then  an  electron  will  get  away 
from  the  illuminated  plate  to  the  surrounding  electrode  only  when 
aided  by  a  suitable  accelerating  field.    Even  when  these  three  effects 
have  been  reduced  to  zero,  the  part  CD  may  still  be  obtained. 


Current 


Retarding 
Potential 


Accelerating 
Potential 


Fig.  7. 


(4)     A  fourth  source  of  this  peculiarity  in  the  curve  has  been 
discovered   by   Richardson   and   Compton1.     The   real   potential 
difference   between  the   illuminated  plate   and  the  surrounding 
electrode  is   that  given   by  the  measuring  instrument  plus  (or 
\minus)  the~XQntact_differ£jice  of  potential  between  them.     Thus 
/the  effective  field  acting  on   the  electrons   involves  the  contact 
I  difference  of  potential.     The  curve,  Fig.  7,  relative  to  the  broken 
ordinate  as  zero  ordinate  is  what  they  obtained  experimentally. 
(The  disturbing  effects  already  discussed  were  avoided  in  Richard- 
son and  Compton's  experiments.)     On  allowing  for  the  contact 
difference  of  potential,  the  zero  ordinate  has  to  be  shifted  by  an 
amount  00'.     The  corrected  ordinate  always  meets  the  curve  where 
it  begins  to  drop.     Hence  all  velocities  from  a  maximum  velocity 
down  to  zero  are  present  and  there  are  no  electrons  which  emerge 
1  Richardson  and  Compton,  Phil.  Mag.  xxiv.  p.  577,  1912. 


Ill]        THE   VELOCITIES   OF    EMISSION    OF   PHOTO- ELECTRONS 


only  with  the  help  of  an  external  field.  Since  the  left-hand  side 
of  the  experimental  curve  (Fig.  7)  gives  the  relation  between  the 
energy  (represented  by  the  voltage)  and  the  number  of  electrons 
possessing  energies  greater  than  that  value,  it  is  clear  that  the 
relative  number  of  electrons  emitted  with  any  given  energy  is 
obtained  by  plotting  the  gradient  of  the  curve  in  Fig.  7  against 
the  retarding  voltage.  In  this  way  the  energy  distribution  curve 
(Fig.  8)  is  obtained  from  the  experimental  curve  (Fig.  7).  It  is  seen 
that  the  energies  are  distributed  symmetrically  about  a  mean  energy. 

Richardson  and  Compton's  curves  were  obtained  with  mono- 
chromatic light.     It  is  easily  seen  that  even  if  photo-electrons 
emerge  from  their  parent  systems  with 
identical    velocities,   outside    the   plate 
there  will  be  a  whote  range  of  velocities 
from  a  maximum  down  to  zero,  owing  to 
the  electrons  losing  energy  in  passing 
from  different  depths  in  the  plate  before 
they  escape  at  the  surface.    It  is  natural 
to     regard     the     maximum     emission 
velocity  deduced  from  experimental  ob- 
servations as  the  real  velocity  of  emission  unaltered  by  collisions 
or  other  causes. 

Even  when  all  the  effects  previously  discussed  are  avoided,  the 
experimental  curves  may  lead  to  incorrect  views  as  to  the  distri- 
bution of  energy  among  the  electrons,  unless  the  apparatus  is  of 


Relative 
Number 


Energy 


Fig.  8. 


IN' 


P 

Fig.  9. 


Current 


Accelerating 
Potential 


Fig.  10. 


suitable  form.  An  example  will  make  this  clear.  Consider  photo- 
electrons  leaving  the  point  P  (Fig.  9)  with  equal  velocities  and  in 
all  directions.  (PP'  and  NN'  are  two  parallel  planes.) 

We  shall  see  that  the  velocity  distribution  curve  found  by 
H-  3 


34  PHOTO-ELECTRICITY  [CHAP. 

experiment  would  not  be  ABC  (Fig.  10)  but  AbC,  which  implies 
on  the  usual  interpretation  that  all  velocities  from  that  corre- 
sponding to  AO  down  to  zero  are  present. 

Let  FO  be  the  potential  required  to  stop  an  electron  projected 
normally  from  the  plate  PPr  by  the  time  it  reaches  the  plate  NN\ 
which  is  at  zero  potential,  The  component  of  the  velocity,  per- 
pendicular to  the  plate,  of  an  electron  which  leaves  the  plate  at  an 
angle  0  with  the  normal  is  proportional  to  cos  9  and  the  kinetic 
energy  associated  with  this  component  is  therefore  proportional  to 
cos2  0.  Hence  the  potential  required  to  turn  the  electron  so  that 
it  just  grazes  the  plate  NNf  is  F0  cos2  0.  If  this  potential  difference 
be  applied,  only  those  electrons  which  leave  PP'  at  an  angle  with 
the  normal  less  than  6  will  reach  the  plane  NN'.  If  n  be  the 
number  of  electrons  leaving  unit  area  of  the  plate  PP'  through 
unit  solid  angle,  the  number  leaving  the  plate  at  an  angle  less 
than  6  will  be  proportional  to 


,  I*  siu6d0  or  n(l  -cos  0). 

Jo 


Thus  a  number  of  electrons  proportional  to  1  —  cos  6  have  a  mini- 
mum apparent  energy  proportional  to  cos20.  Therefore  the 
relation  between  the  number  of  electrons  which  appear  to  possess 
energies  above  a  certain  amount,  and  that  amount,  is  parabolic. 
The  experimental  curve  AbCD  has  no  resemblance  to  the  curve 
ABCD  from  which  the  true  distribution  of  energies  can  be  obtained. 
Though  this  is  an  extreme  case,  it  illustrates  the  caution  one 
must  observe  in  discussing  so-called  velocity  distribution  curves. 
Whenever  an  electron  approaches  a  boundary  with  an  appreciable 
tangential  velocity,  then  the  potential  difference  just  necessary  to 
stop  it  is  less  than  the  potential  which  corresponds  to  its  actual 
velocity.  In  Richardson  and  Compton's  arrangement,  in  which  a 
small  illuminated  plate  was  surrounded  by  a  large  spherical 
electrode  so  that  the  field  was  radial,  this  effect  was  avoided  and 
therefore  the  true  distribution  of  energies  could  be  obtained 
immediately  from  the  experimental  curve. 

Van  der  Bijl1  has  shown  lately  how  easily  misleading  energy 
distribution  curves  can  be  obtained  and  has  confirmed  Richardson 
and  Compton's  discovery  of  the  influence  of  contact  potential. 

1  Van  der  Bijl,  Verh.  d.  Deutsch.  Phys.  Ges.  xv.  p.  330,  1913. 


Ill]       THE   VELOCITIES   OF   EMISSION   OF   PHOTO-ELECTRONS 


35 


Experimental  Results. 

Ladenburg1  was  the  first  to  investigate  the  relation  between  the 
maximum  emission  velocities  of  the  photo-electrons  and  the  wave- 
length of  the  light.  The  metals  used  were  Pt,  Zn  and  Cu.  They 
were  unavoidably  exposed  to  the  atmosphere  between  the  time  of 
polishing  and  the  exhaustion  of  the  apparatus.  The  potentials  to 
which  the  plate  rose  when  illumined  by  different  wave-lengths  are 
given  in  the  following  table.  The  maximum  emission  energies  are 
proportional  to  the  potentials  and  the  actual  values  can  always  be 
obtained  by  multiplying  by  e,  the  charge  on  an  electron,  as  in 
equation  (1),  p.  28. 

Ladenburg  found  that  his  results  could  be  represented  by  the 
equation  V  V .  X  =  const.,  where  V  is  proportional  to  the  maximum 
energy.  According  to  this,  the  maximum  velocity  of  emission  is 
proportional  to  the  frequency,  or  the  maximum  energy  is  propor- 
tional to  the  square  of  the  frequency. 

TABLE  1. 


Potentials  measuring  the  maximum 

emission  energies 

Wave-length 

Pt 

Cu 

Zn 

X2600 

1-075  vohs 

1-01  volts 

•685  volts 

X2420 

1-28       „ 

1-16     „ 

•79       „ 

X2290 

1-49       „ 

1-33     „ 

•95       „ 

X2180 

1-60       „ 

1-46      „ 

1-00       „ 

X2100 

176       „ 

1-55      „ 

1-07       „ 

X2010 

1-86       „ 

1-69     „ 

1-12       „ 

Joffe'2  showed  that  Ladenburg's  results  would  satisfy  equally 
well  the  law  that  the  energy  (velocity  squared)  was  a  linear  function 
of  the  frequency.  The  range  of  wave-lengths  used  by  Ladenburg 
was  too  small  to  determine  whether  the  results  lie  on  a  straight 
line  or  on  a  short  piece  of  a  parabola,  a  long  way  from  the  vertex. 

It  will  be  observed  that  the  more  electropositive  the  metal,  the 
smaller  the  velocities.  Ladenburg  did  not  allow  for  the  contact 

1  Ladenburg,  Verh.  d.  Deutsch.  Phys,  Ges.  ix.  p.  504,  1907. 

2  Joffe",  Ann.  d.  Phys.  xxiv.  p.  939,  1907. 

3—2 


36  PHOTO-ELECTRICITY  [CHAP. 

potential  difference  which  accounts  in  part,  if  not  wholly,  for  the 
order  of  the  velocities  recorded. 

Millikan  and  Winchester1  investigated  the  emission  velocities 
of  photo-electrons  from  eleven  metals.  The  metals  were  polished 
with  dry  emery,  washed  with  alcohol  and  then  dried.  As  in 
Ladenburg's  experiments,  they  were*  in  contact  with  the  atmo- 
sphere for  some  time  before  the  necessary  vacuum  could  be 
obtained  in  the  apparatus.  The  unresolved  light  from  a  spark 
•/as  used  and  passed  through  air  and  a  quartz  plate.  Hence  the 
shortest  available  wave-length  exceeded  A 1750.  The  order  of 
velocities  found  was  appreciably  different  from  that  given  by 
Ladenburg.  This  must  be  attributed  to  slight  differences  in  the 
treatment  of  the  surfaces,  which  has  an  important  influence  in 
photo-electric  experiments. 

Attempts  of  various  kinds  were  made  by  different  experi- 
menters to  avoid  complications  arising  from  surface  films.  It  was 
at  one  time  thought  that  treating  a  surface  as  cathode  in  a 
discharge  at  low  pressures,  so  that  the  exterior  was  removed  by 
sputtering,  would  expose  a  new  uncontaminated  surface  suitable 
for  photo-electric  experiments.  Using  such  surfaces,  von  Baeyer 
and  Gehrts2  found  that  energies  as  high  as  6  volts  could  be 
obtained,  and  moreover,  that  the  energies  were  identical  for  Au, 
Al  and  Pt.  This  energy  was  considered  to  be  the  real  energy  of 
emission  from  the  molecule.  From  similar  experiments,  the  author s 
concluded  that  using  the  plate  as  cathode  or  anode  merely  resulted 
in  an  accelerating  (sometimes  a  retarding)  layer  being  formed  on 
the  plate.  The  charged  ions  travelling  to  and  from  the  plate 
during  the  discharge  may  easily  give  rise  to  charged  layers  on  the 
surface.  That  this  explanation  is  the  true  one  was  verified  later 
by  von  Baeyer  and  Tool4,  who  found  that  they  could  get  the 
maximum  emission  energies  to  go  up  to  30  volts  by  more  drastic 
treatment  of  the  plate. 

Klages5  worked  with  a  mercury  surface  which  could  be  renewed 
in  vacuo.  ,  Using  the  light  from  a  mercury  lamp,  he  obtained 

1  Millikan  and  Winchester,  Phil.  Mag.  xiv.  p.  188,  1907. 

2  von  Baeyer  and  Gehrts,  Verh.  d.  DeutscJi.  Phys.  Ges.  xn.  p.  870,  1910. 

3  Hughes,  Proc.  Camb.  Phil.  Soc.  xvi.  p.  167,  1911. 

4  von  Baeyer  and  Tool,  Verh.  d.  Deutsch.  Phys.  Ges.  xm.  p.  569,  1911. 

5  Klages,  Ann.  d.  Phys.  xxxi.  p.  343,  1910. 


Ill]        THE   VELOCITIES   OF   EMISSION  OF   PHOTO-ELECTRONS  37 

maximum  emission  energies  corresponding  to  2'3  volts.  The 
shortest  wave-length  was  probably  X1849. 

Kunz1  concluded  that  his  experiments  on  sodium-potassium 
alloy  and  on  caesium  were  in  better  agreement  with  Ladenburg's 
law  than  with  the  energy  law.  Cornelius2  investigated  the  effect 
for  potassium  and  concluded  that  his  experimental  results  were 
represented  by  a  linear  relation  between  the  velocity  and  the 
frequency.  The  experimental  arrangements  in  the  experiments 
of  Kunz  and  Cornelius  do  not  seem  to  be  satisfactory  and  no  doubt 
affect  the  accuracy  of  their  results.  It  should  be  mentioned  that 
photo-electric  experiments  on  the  alkali  metals  are  extremely 
difficult  on  account  of  the  great  susceptibility  of  these  metals  to 
contamination.  For  further  discussion  of  these  experiments,  the 
reader  is  referred  to  Compton3. 

Millikan  and  Wright4  have  published  a  number  of  researches 
in  which  they  experimented  on  metals  which  were  kept  for  a  very 
long  time  in  the  highest  vacua  and  which  were  illuminated  for 
long  periods  by  intense  ultra-violet  light.  The  result  of  this 
treatment  was  in  general  to  increase  the  maximum  emission 
energies  from  the  normal  2  volts  to  about  15  or  20  volts.  The 
explanation  offered  by  Millikan  and  Winchester  is  that  this  treat- 
ment removes  a  surface  film  and  that  the  electrons  then  emerge 
with  their  true  velocities.  More  recent  experimental  investigations 
suggest  that  these  high  emission  energies  are  due  to  accelerating 
films  formed  in  some  way  on  the  surface.  To  test  this,  the  con- 
tact potential  difference  should  be  measured  during  the  course  of 
the  experiment.  It  is  probable  that  the  changes  in  the  contact 
potential  difference  would  run  parallel  with  the  change  in  the 
emission  energies. 

The  inconsistencies  of  previous  results  led  the  author5  to  make 
a  series  of  experiments  on  metallic  surfaces  prepared  by  distilla- 
tion in  vacuo.  In  this  way  the  formation  of  the  troublesome  surface 
films  was  avoided.  Much  more  consistent  results  were  obtained 
than  with  ordinary  polished  surfaces.  Careful  measurements 

1  Kunz,  Phys.  Rev.  xxix.  p.  3,  1909 ;  xxxi.  p.  536,  1910. 

2  Cornelius,  Phys.  Rev.  (2)  i.  p.  16,  1913. 

3  Compton,  Phys.  Eev.  (2)  i.  p.  382,  1913. 

4  Millikan  and  Wright,  Phys.  Eev.  xxx.  p.  287,  1910 ;  xxxiv.  p.  68,  1912. 

5  Hughes,  Phil.  Trans.  A.  ccxii.  p.  205,  1912. 


38 


PHOTO-ELECTRICITY 


[CHAP. 


were  made  to  decide  definitely,  if  possible,  whether  the  maxi- 
mum emission  velocity,  or  the  maximum  emission  energy,  is 
proportional  to  the  frequency.  The  apparatus  used  is  shown  in 
Fig.  11.  The  illuminated  plate  N  was  in  metallic  connection  with 


Fig.  11. 

the  tilted  electroscope.  Monochromatic  light  fell  upon  it,  and  the 
potential  to  which  it  rose  under  illumination  was  given  by  the 
electroscope.  From  this  potential  the  maximum  emission  energy 
could  be  calculated.  The  metal  to  be  distilled  was  contained  in 


Ill]        THE   VELOCITIES  OF   EMISSION   OF   PHOTO-ELECTRONS 


39 


the  quartz  furnace  F.  By  means  of  the  winch  E,  the  plate  N 
could  be  lowered  until  it  was  near  F  so  that  the  volatilized  metal 
condensed  on  it.  From  the  time  of  formation  to  the  time  of 
illumination,  the  metallic  surface  was  in  the  best  vacuum  obtain- 
able by  the  liquid  air  method.  The  results  for  distilled  cadmium 
are  given  in  Table  2. 

TABLE  2. 


Wave-length 

Experimental  potentials  measuring 
the  maximum  emission  energies 

Mean  potentials 

X2537 

•901              -901               -890* 

•897  volts 

X2257 
X1849 

1-420            1-431             1-431 
2-480            2-480            2-480 

1-427     „ 
2-480     „ 

Wave-length 

Frequency  n 

Experimental         v    ,       v 
potentials  V 

*Jv=k'n-c 

X1849 
X2257 
X2537 

1623  x  1012 
1329     „ 
1182     „ 

2-480  volts              [2-480] 
1-427     „                   1-424 
•897     „                   [-897] 

[2-480] 
1-339 
[-897] 

X2967 
X3126 
X3340 

1010    „ 

960    „ 
898    „ 

•148     „                     -286 
0        „                     -101 
No  effect           (  -  -12) 

•495 
•398 
•293 

Constants  in  V=  kn  -  V0,     V0 = 3  347  volts,     k = 3'590  x  10 ~ 15. 

In  the  fourth  and  fifth  columns  we  have  the  theoretical  values 
for  the  potentials  corresponding  to  the  maximum  energies  calcu- 
lated on  the  energy  law  and  on  the  velocity  law  respectively.  The 
two  values  in  square  brackets  were  used  to  determine  the  constants. 

The  proof  of  the  linear  relation  between  the  maximum  energy 
and  the  frequency  depends  mainly  on  careful  observations  re- 
corded for  X1849,  X2257  and  X.2537.  Comparing  the  third  and 
fourth  columns,  we  see  that  the  experimental  potential  and  the 
theoretical  potential,  calculated  on  the  energy  law,  for  X2257 
agree  to  '003  volt.  On  the  other  hand  there  is  a  difference  of 
'083  volt  between  the  experimental  potential  and  that  calculated 
on  the  velocity  law.  Additional  confirmation  is  supplied  by  the 
fact  that  the  photo-electric  eflfect  sets  in  between  \3126  and 
X3340  which  agrees  with  the  energy  law  but  not  with  the  velocity 
law.  (The  velocities  corresponding  to  X2967  and  X3126  are 


40 


PHOTO-ELECTRICITY 


[CHAP. 


smaller  than  the  predicted  values  on  account  of  the  earth's  mag- 
netic field  being  sufficient  to  cause  the  slow  electrons  to  describe 
almost  complete  circles  inside  the  apparatus.) 

For  each  metal,  several  tables  similar  to  that  given  above  .were 
obtained  and  in  every  case  the  energy  law  was  verified.  ^^ 

The  results  are  summarized  in  the  following  table.  The  linear 
relation,  V=kn—  F0,  connecting  the  energy  and  the  frequency  is 
completely  characterized  by  the  constants  k  and  F0.  Hence  the 
experimental  velocities,  corresponding  to  any  wave-length,  can  be 
deduced  readily.  When  V  is  plotted  against  n,  the  intersection 
of  the  line  with  the  axis  of  abscissae  determines  the  wave-length 
\0  at  which  the  effect  sets  in. 

TABLE  3. 


Element 

Atomic 
weight 

Atomic 
volume 

Valency 

k 

Fo 

Xo 

Ca 

40-1 

25-4 

2 

3-17  x!0~15 

2-57  volts 

3700 

Mg 

24-3 

14-0 

2 

3-39       „ 

3-08     „ 

3300 

Cd 

112-4 

13-0 

2 

3-66       „ 

3-49     „ 

3140 

Zn 

65-4 

9-2 

2 

3-79       „ 

3-77     „ 

3016 

Pb 

207-1 

18-1 

4 

3-55       „ 

3-42     „ 

3115 

Bi 

208-0 

21-2 

5 

3-63       „ 

3-37     „ 

3233 

Sb 

120-2 

18-1 

5 

3-69       „ 

3-60     „ 

3075 

As 

75-0 

13-1 

5 

^  3-7       „ 

^4-5     „ 

2360 

Se 

79-2 

17-6 

6 

^4-8     „ 

=0:2200 

02 

16-0 

12-6 

6 

=2=8-0     „ 

1350 

Note.  The  constants  F0  for  Se  and  O2  were  obtained  indirectly.  As  k 
does  not  vary  much,  a  mean  value  3 -66  x  10  ~15  was  taken  and  the  velocity  for 
Se  corresponding  to  X  1849  was  determined.  For  O2  the  wave-length  at 
which  the  ionisation  sets  in  was  assumed  to  be  X  1350.  Taking  the  mean 
value  of  k  again  we  get  F0=8  volts.  For  further  observations  on  the  ionising 
potential  for  O2  see  p.  20. 

The  values  of  k  and  F0  appear  to  change  regularly  with  the 
atomic  volumes  for  elements  of  the  same  valejicy,  but  there  is 
a  discontinuity  (always  in  the  same  direction  however)  as  we  pass 
from  one  valency  to  another.  The  connection  with  the  atomic 
volume  is  much  more  marked  than  with  the  atomic  weight  (cf. 
Ca,  Mg.  Zn,  and  Cd).  The  variations  in  k  are  much  smaller  than 
those  in  F0,  but  they  are  somewhat  bigger  than  the  possible  errors 


Ill]        THE   VELOCITIES   OF   EMISSION   OF   PHOTO-ELECTRONS  41 

of  experiment.     Moreover  they  change  regularly  with  the  atomic 
volume  in  the  same  way  as  V0. 

Richardson  and  Compton1  carried  out  an  important  investiga- 
tion on  the  emission  velocities  of  photo-electrons.  To  obtain  the 
real  emission  velocities,  they  allowed  for  the  contact  potential 
between  the  illuminated  surface  and  the  surrounding  electrode. 
The  maximum  emission  energy  was  a  linear  function  of  the 
frequency,  thus  independently  confirming  the  conclusions  arrived 
JatTy  the  author.  For  each  wave-length,  both  the  maximum 
emission  energy  and  the  mean  energy  of  the  photo-electrons  were 
determined.  Richardson  and  Compton  consider  the  determination 
of  the  mean  energies  to  be  rather  more  accurate  and  prefer  to 
employ  them  in  deducing  the  characteristic  X0  for  each  metal. 
The  gradient  k  of  the  line  connecting  the  maximum  energy  and 
the  frequency  is  about  the  same  for  Na,  Al,  Mg,  Zn,  Sn,  and  Pt. 
The  authors  consider  the  small  variations  in  k  to  be  accidental  and 
within  the  errors  of  experiment,  and  so  no  relation  between  k  and 
some  other  property  of  the  atom  was  looked  for.  They  obtained 
a  considerably  smaller  gradient  for  Cu  and  Bi,  for  which  no 
explanation  is  offered.  Their  results  are  summarized  in  the 
following  table : 

TABLE  4. 


Values  from  maximum  energies 

Values  from  mean  energies 

Metal 

k                            Xo 

k' 

V 

Na 

3-3X10-1* 

5830 

l-7xlO~15 

5770 

Al 

2-8 

4770 

1'7       „ 

4110 

Mg 

3-3 

3820 

1-6       „ 

3750 

Zn 

3-2 

3760 

1-8      „ 

3570 

Sn 

3-1 

3620 

1-8 

3370 

Bi 

2-3 

3300                1-2       „ 

3370 

Cu 

2-4 

3000                 1-1       „ 

3090 

Pt 

375     „ 

2800 

1-8       „ 

2910 

The  units  of  k  are  the  same  as  those  in  Table  3.     kf  is  very  nearly  %k  on 

the  whole,  hence  the  energies  are  distributed  equally  about  the  mean  energy, 

or  the  curve  in  Fig.  8  is  symmetrical.     The  values  of  X0  given  by  Richardson 

and  Compton  are  somewhat  greater  than  those  given  by  the  author  in  Table  3. 

1  Eichardson  and  Compton,  Phil.  Mag.  xxiv.  p.  576,  1912. 


42  PHOTO-ELECTRICITY  [CHAP. 

An  interesting  point  relating  to  contact  potential  arises  out  of 
a  comparison  of  the  two  researches  just  discussed.  The  velocities 
of  photo-electrons  from  say  Zn,  as  usually  determined,  are  less 
than  the  velocities  from  the  more  electronegative  elements  (e.g. 
Table  1).  On  allowing  for  the  contact  potential  difference  (as  in 
Richardson  and  Compton's  work)  it  is  found  that  the  order  of  the 
velocities  is  inverted.  But  the  order  of  the  velocities  from  dis- 
tilled metals  is  in  better  agreement  with  the  velocities  corrected 
for  contact  potential  than  with  the  uncorrected  velocities.  This 
suggests  that  there  should  be  little  or  no  contact  potential 
difference  between  metals  distilled  in  vacuo  and  consequently 
that  the  ordinary  contact  potential  arises  directly  from  the 
differential  effect  of  air  (or  other  gases)  on  metallic  surfaces. 

^^^ Effect  of  Temperature  on  Emission  Velocities  of 
Photo- Electrons. 

Several  investigators  have  made  experiments  to  see  whether 

the  maximum  velocities  of  emission   of  photo-electrons  depend 

upon  the  temperature   of  the  illuminated  surface.     Ladenburg1 

found  that  the  velocities  of  the  photo-electrons  from  Au,  Pt  and  Ir 

were  independent  of  the  temperature  up  to  800°  C.     Kunz2  found 

this  to  be  the  case  for  Na-K  alloy  (no  temperature  range  given), 

Millikan  and  Winchester3  for  eleven  metals  from  15°  to  125°,  and 

"  Lienhop4  for  temperatures  down  to  -  180°.     It  may  therefore  be 

\  concluded  that  the  velocities  of  emission  of  photo-electrons  are 

I  independent  of  the  temperature  of  the  illuminated  surface  over 

f  a  wide  range. 

Theories  of  the  Photo- Electric  Effect. 

Quantum  theory.  From  the  two  researches  discussed  above,  it 
may  be  concluded  that  the  linear  relation  between  the  maximum 
emission  energy  and  the  frequency  has  now  been  established 
definitely.  There  is  still,  however,  some  obscurity  as  to  the 
interpretation  of  the  gradient  of  the  line,  V  =  kn—  V0.  The 

1  Ladenburg,  Verh.  d.  Deutsch.  Phys.  Ges.  ix.  p.  165,  1907. 

2  Kunz,  Phys.  Rev.  xxix.  p.  174,  1909. 

3  Millikan  and  Winchester,  Phil.  Mag.  xiv.  p.  188,  1907. 

4  Lienhop,  Ann.  d.  Phys.  xxi.  p.  281,  1906. 


Ill]        THE   VELOCITIES  OF   EMISSION   OF  PHOTO-ELECTRONS  43 

quantum  theory  of  light  was  first  applied  to  the  photo-electric 
effect  by  Einstein1.  If  the  energy  in  the  quantum  hn  is  wholly 
transferred  to  the  photo-electron,  then  we  have 

Ve  =  hn, 

and  if  by  the  time  the  electron  emerges  it  has  lost  an  amount  of 
energy  VQe,  then 

V=(h/e)n-V0. 

This  at  once  leads  to  the  correct  variation  of  V  with  n.  The 
coefficient  of  n  is  h/e  and  is  numerically  equal  to  419  x  10~15  if  we 
take  h  =  6'55  x  1Q-*7,  e  =  4'65  x  1Q-10  E.s.u.  and  V  in  volts.  The 
actual  values  of  the  coefficient  determined  experimentally  range 
from  317  to  3'79  x  10~15  (Table  3).  Had  the  experimental  values 
of  k  been  grouped  about  the  theoretical  value  h/e,  it  would  have 
been  natural  to  conclude  that  k  is  probably  constant  for  all  metals 
and  equal  to  the  quotient  of  these  two  universal  constants.  How- 
ever the  experimental  values  are  well  outside  the  theoretical  value. 
There  is  no  reason  on  the  quantum  theory  why  all  the  energy  in 
the  quantum  hn  should  be  acquired  by  the  photo-electron ;  it  may 
be  shared  between  the  electron  and  its  parent  molecule  and  the 
sharing  may  depend  upon  the  nature  of  the  molecule,  thus  giving 
rise  to  variations  in  k. 

Yet  the  common  occurrence  of  this  constant  h  in  so  many 
branches  of  physics  prevents  us  from  dismissing  finally  the  possi- 
bility that,  though  the  experimental  results  are  represented  by 
V  =  kn—V0,  yet  the  more  fundamental  underlying  process  is 
represented  by  V  =  (h/e)n—V0.  Let  us  see  how  this  could  arise. 
The  change  from  one  to  the  other  could  be  attributed  to  some 
process  which  reduces  the  energies  of  the  photo-electrons  in  the 
same  proportion.  .This  would  mean  that  the  reduction  in  the 
energy  would  be  proportional  to  the  energy.  It  is  difficult  to 
imagine  any  such  process.  A  surface  layer  would  reduce  all  the 
energies  by  the  same  amount.  The  author  (loc.  cit.)  found  that 
the  effect  of  admitting  oxygen  to  a  distilled  surface  of  Cd  was  to 
shift  the  line  V—kn  —  VQ  parallel  to  itself.  Again  the  mean  k 
was  about  16  %  less  than  hie  and  in  Richardson  and  Compton's 
experiments  about  20  %  less-  Yet,  though  there  was  a  great 

1  Einstein,  Ann.  d.  Phys.  xvn.  p.  132,  1905. 


44  PHOTO-ELECTRICITY  [CHAP. 

difference  in  the  state  of  the  surfaces  in  the  two  researches,  this 
did  not  seem  to  affect  the  value  of  k  to  any  great  extent. 

A  way  of  reconciling  the  theoretical  and  experimental  results 
may  be  based  on  the  fact  that  the  emission  energies  of  the  photo- 
electrons  emitted  from  a  thin  film  are  greater  when  they  are 
emitted  in  the  same  direction  as  that  in  which  the  light  is 
travelling  than  when  they  are  emitted  in  the  opposite  direction. 
Robinson1  found  that  the  maximum  energy  on  the  emergent 
side  of  a  thin  platinum  film  exceeded  that  on  the  incident  side  by 
about  12  %.  Taking  ke  for  Pt  to  be  5'85  x  1Q-27  from  Richardson 
and  Comp ton's  experiments  and  increasing  this  by  12  °/0,  we  get 
6 '5 5  x  10~27,  which  is  in  numerical  agreement  with  Planck's  con- 
stant. Possibly  the  photo-electrons  are  emitted  from  their  parent 
systems  in  the  same  direction  as  that  of  the  incident  light, 
and  those  which  emerge  from  the  illuminated  surface  in  the 
opposite  direction  lose  energy  when  their  direction  of  motion  is 
changed.  Thus  we  should  expect  the  maximum  velocities  of 
photo-electrons  emitted  from  sheets  of  metal  in  a  direction  opposite 
to  that  of  the  incident  light  to  be  less  than  the  theoretical  values. 
More  work  on  thin  films  is  necessary  before  this  explanation  can 
be  regarded  as  established.  This  single  observation  of  Robinson 
on  platinum  is  very  suggestive  and  similar  investigations  should 
be  extended  to  other  metals. 

It  is  instructive  to  compare  the  value  of  VQe  deduced  from 
photo-electric  experiments  with  values  of  the  work  done  by  an 
electron  in  escaping  from  a  hot  metal.  Richardson  gives  5*34  volts 
as  representing  the  work  done  (per  unit  charge)  when  an  electron 
escapes  from  hot  platinum.  The  results  given  in  Table  4  indicate 
that  F0  for  platinum  is  3*86  volts  calculated  from  V—  kn  —  F0. 
Even  if  we  use  F=  (h/e)  n  —  F0  instead,  and  assume  that  the  photo- 
electric effect  starts  at  A,  2910,  F0  only  increases  to  4'32  volts. 
It  is  possible  that  F0  varies  slowly  with  the  temperature  though 
there  appears  to  be  no  evidence  for  this  either  in  photo-electric  or 
in  thermionic  experiments.  Of  course  the  assumption  is  here 
made  that  electrons  of  the  same  kind  are  released  in  both  effects. 
The  free  electrons  are  concerned  in  the  thermionic  experiments,  it  is 
not  so  certain  that  they  are  involved  in  photo-electric  experiments. 

1  Kobinson,  Phil.  Mag.  xxv.  p.  115,  1913. 


Ill]       THE   VELOCITIES   OF   EMISSION   OF   PHOTO-ELECTRONS  45 

There  is  no  need  to  suppose  that  the  explanation  of  the  photo- 
electric effect  on  the  quantum  theory  necessarily  means  that  light 
is  molecular  in  structure,  though  at  one  period  it  was  assumed 
that  such  was  the  case.  Attempts  have  been  recently  made  to 
account  for  the  results  of  the  quantum  theory  in  ways  which  do  not 
require  the  assumption  of  a  molecular  structure  in  radiant  energy1. 

**  Richardson's  Statistical  Theory. 

Richardson2  offers  a  theory  of  photo-electric  phenomena  based 
on  thermodynamical  and  statistical  principles.  Consider  a  cavity 
in  a  piece  of  matter.  Inside  the  cavity  there  is  an  atmosphere  of 
electrons,  the  concentration  of  the  electrons  being  a  function  of  the 
temperature.  Richardson  finds  that 

/»* 

n  =  Ae 

is  the  relation  between  the  concentration  of  electrons  and  the 

temperature,  where 

n  is  the  number  of  electrons  per  c.c.  in  the  atmosphere, 
A  a  constant  depending  on  the  nature  of  the  matter, 
E  the  gas  constant  for  a  single  electron 

(hence  the  kinetic  energy  of  an  electron  is  f  R6) 

and    w      the  latent  heat  of  evaporation  of  an  electron  in  ergs. 

The  usual  methods  of  the  kinetic  theory  of  gases  show  that  the 

number  of  electrons  returning  to  the  matter  from  the  atmosphere 

per  sec.  is  N  =  $nd~*,  where  yS  is  a  number  calculated  on  the 

kinetic  theory.     Thus 

f  w  w° 

on  substituting 


where  w0  is  the  work  done  by  the  electron  against  the  forces 
tending  to  retain  it  in  the  matter. 

1  In   a    recent  paper   (Phil   Mag.  xxvi.    p.   792,    1913)    Sir  J.    J.   Thomson 
describes  a  model  of  the  atom  which  leads  to  a  number  of  results  indicated  by  the 
quantum  theory  without  the  necessity  of  assuming  that  a  wave  front  of  light  is 
discontinuous  in  structure.     Among  the  results  accounted  for  by  this  model  is  the 
relation  between  the  energy  and  frequency  in  the  photo-electric  effect. 

2  Richardson,  Phil.  Mag.  xxm.  p.  594,  1912 ;  xxrv.  p.  574,  1912. 


46  PHOTO-ELECTRICITY  [CHAP. 

Having  calculated  the  number  of  electrons  which  arrive  at  the 
surface,  "Richardson  proceeds  to  calculate  the  number  which  leave 
it.  Let  the  energy  density  of  the  complete  aetherial  radiation 
which  is  in  equilibrium  with  the  matter  at  temperature  0,  between 
the  frequencies  n  and  n  +  dn,  be 

E  (n,  6)  dn, 

where  E  (n,  0)  is  some  function  of  n  and  0.  The  rate  of  absorp- 
tion is 

-^E(n,e)dnt 

where  c  is  the  velocity  of  light  and  e  the  emissivity.  The  assump- 
tion is  now  made  that  the  emission  or  absorption  of  unit  quantity 
of  radiant  energy  of  frequency  n  causes*  the  liberation  of  F  (n) 
electrons.  The  total  number  of  electrons  emitted  in  unit  time  by 
the  complete  radiation  is 


:/, 


.    [">*«•.•>* w 

Equations   (3)   and   (4)   must  be   identical   for   all  values   of  0. 
Richardson  employed  Wien's  formula  for  the  complete  radiation 

_7m 

E  (n,  0}  =  — —  hn?e 
c* 

The  equation  to  be  solved  is  therefore 

hn  wtt 


o 
all  the  constants  being  included  in  A^.     The  equation  is  satisfied 

by 

€F  (n)  =  0  when  0  <  hn  <  w0 

„,  .      AJi  (        w0\      ,  j  [ (5). 

and  eF(n)  =  -^— 2  (  1  —  T—  )  when  WQ  <  hn  <  oo 

JAj  TL     \  fl'lL/ 

Hence  there  is  no  photo-electric  emission  with  frequencies  less 
than  w0/h.  No  experimental  evidence  is  available  for  testing 
the  predicted  relation  between  the  number  emitted  and  the 
frequency1. 

If  the  mean  kinetic  energy  of  the  electrons  which  are  emitted 

1  See  however  a  recent  paper  by  Compton  arid  Kichardson  (Phil.  Mag.  xxvi. 
p.  549,  1913). 


Ill]       THE   VELOCITIES   OF   EMISSION   OF   PHOTO-ELECTRONS  47 

by  light  of  frequency  n  is  Tn,  then  the  total  energy  E  emitted 
under  the  influence  of  the  complete  radiation  is 


£ 


E=\\    TneF(n).E(n,0)dn. 

The  JV  electrons  streaming  inwards  from  the  atmosphere  bring 
with  them  2NR0  units  of  energy  per  sec.  Hence,  substituting 
for  N,  we  must  have 

hn  hn 

OT5/J  J?/J 

TneF(n)hn*e         dn     ~'   ~~ 
. 

Provided  that  eF(n)  is  expressed  as  in  (5),  the  solution  is 
Tn  =  hn  -  w0  when  w0  <  hn  <  x  . 

This  gives  a  linear  relation  between  the  maximum  emission 
energy  and  the  frequency  as  found  by  experiment.  As  a  rule 
electrons  lose  energy  by  collisions  in  emerging  and  hence  the 
presence  of  large  numbers  with  velocities  less  than  the  maximum. 
Richardson  points  out  that  this  theory  does  not  involve  the 
assumption  that  radiant  energy  is  molecular  in  structure  except  in 
so  far  as  it  is  implied  in  Wien's  formula. 

The  statistical  method  gives  no  insight  into  the  processes  at 
work  in  ionisation  by  light.  It  is  concerned  only  with  deductions 
which  can  be  made  from  the  consideration  of  energy  interchanges 
on  a  large  scale,  and  not  with  those  associated  with  individual 
molecules  and  electrons.  Moreover  the  theory  is  developed  under 
the  assumption  that  the  substance  is  in  thermal  equilibrium  with 
complete  radiation  travelling  with  equal  intensities  in  all  direc- 
tions. The  experimental  results  are  obtained  with  directed 
monochromatic  light. 

Photo- Electric  Effect  as  a  Resonance  Phenomenon. 

The  explanation  of  the  photo-electric  effect  on  Einstein's 
quantum  theory  and  on  Richardson's  statistical  theory,  while 
leading  to  results  in  good  agreement  with  experiment,  gives 
us  no  indication  of  the  actual  process  which  occurs.  A  theory, 
which  makes  some  attempt  to  represent,  more  or  less,  the  actual 
mechanism  of  the  photo-electric  effect,  is  in  many  ways  more 
satisfactory  to  physicists  than  those  theories  which  by  their 


48  PHOTO-ELECTRICITY  [CHAP. 

nature  are  only  concerned  with  energy  interchanges  and  not  with 
the  individual  molecules  and  electrons.  All  theories  which  deal 
with  the  actual  mechanism  of  the  photo-electric  effect  are  based 
on  some  kind  of  resonance  process.  The  undoubted  complexity  of 
atomic  systems  does  not  permit  an  accurate  picture  of  the  resonant 
system  to  be  formed.  The  various  resonant  systems  which  are 
designed  to  meet  the  experimental  results  probably  do  not  occur 
in  their  simple  isolated  forms  in  nature.  Nevertheless  these 
hypothetical  systems  are  of  considerable  value  and  help  in  indi- 
cating the  principal  features  of  the  actual  systems  responsible  for 
the  photo-electric  effect. 

As  Lenard1  pointed  out,  a  simple  linear  system  is  inadequate  to 
account  for  the  facts.  Imagine  an  electron  capable  of  vibrating 
along  a  line  being  attracted  towards  a  centre  by  a  force  varying 
directly  as  the  distance.  This  system  will  respond  to  a  train  of 
waves  of  the  same  frequency  passing  over  it.  If  we  suppose  that 
the  electron  breaks  away  when  the  amplitude  exceeds  a  certain 
critical  value,  then  it  is  evident  that  the  emission  energy  will 
depend  upon  the  energy  acquired  during  the  last  half-period.  This 
obviously  depends  on  the  light  intensity  and  is  therefore  in  con- 
tradiction with  experiment.  Lenard  suggests  that  the  process  is 
most  probably  one  in  which  the  light  in  some  way  releases  an 
electron  whose  energy  is  determined  by  the  energy  it  had  in  its 
orbit  and  not  to  any  appreciable  extent  by  the  energy  in  the  light 
beam.  In  other  words,  the  light  acts  as  a  kind  of  trigger,  pre- 
cipitating a  state  of  instability  in  certain  atomic  systems  resulting 
in  the  ejection  of  an  electron. 

One  way  of  avoiding  the  objection  made  to  the  linear  system 
is  to  consider  an  electron  describing  circular  harmonic  motion. 
Let  us  assume  that  at  a  distance  R  from  the  centre,  the  force 
stops,  and  that  an  electron  which  describes  increasing  circles  will 
shoot  out  tangentially  when  it  gets  to  this  limiting  distance.  We 
have  the  ordinary  equation  for  circular  harmonic  motion 


—  Fer, 

whence  2?r/i  ==  co  =  \/  —  , 

V   ra 

1  Lenard,  Ann.  d.  Phys.  vm.  p.  149,  1902. 


Ill]        THE   VELOCITIES   OF    EMISSION   OF   PHOTO-ELECTRONS  49 

where  n  is  the  frequency, 

ft>  the  angular  velocity, 
and      F  the  force  on  unit  charge  at  unit  distance. 

To  satisfy  the  experimental  result  we  must  have 

const,  x  n, 


FxP? 

or  —  =  const. 

n 

Assuming  F  to  be  a  constant,  we  see  that  the  critical  radius,  or 
the  distance  of  the  boundary,  must  vary  as  ?i%  or  assuming  the 
critical  radius  to  be  the  same  for  all  systems,  the  intensity  F  of 
force  at  unit  distance  must  increase  as  n.  No  reason  can  be  given 
for  regarding  either  condition  as  likely  to  occur  actually.  (Strictly 
speaking,  the  amplitude  of  the  electron  in  the  system  we  are  now 
considering  would  only  increase  in  the  manner  implied  above  with 
circularly  polarised  light.)  A  formidable  objection  to  this  system 
is  the  following.  Experiment  shows  that  there  must  be  systems 
capable  of  responding  to  all  frequencies  greater  than  a  certain 
frequency.  It  is  difficult  to  imagine  any  atom  containing  the 
large  number  of  systems  necessary  for  the  purpose.  Possibly,  the 
charges  in  the  atom  are  continually  rearranging  themselves  and  so 
F  may  fluctuate  over  a  wide  range  of  values.  Thus  a  small  pro- 
portion of  atomic  systems  may  at  any  given  instant  be  isochronous 
with  light  passing  over  them.  Since  ionised  molecules  are  ex- 
ceedingly few  compared  with  unionised  molecules,  it  suggests  that 
those  which  are  ionised  must  have  been  at  the  moment  of  ionisa- 
tion  in  a  very  special  condition,  for  if  we  assume  the  wave  front 
continuous,  the  state  of  the  particular  molecules  can  be  the  only 
thing  which  determines  whether  ionisation  is  to  happen  or  not. 

A  field  of  force  varying  as  some  inverse  power  of  the  distance 
gives  the  condition  that  orbits  of  all  periods  are  possible  according 
to  the  distance  from  the  centre.  To  satisfy  the  experimental 
results  we  must  have 

^mv2  or  ^mi^co*  =  const,  x  o>, 

TTT 

also  the  law  of  force  wiro>2  =  —  . 

Hence  n  =  3.     We  must,  however,  take  into  account  the  loss  of 
H.  4 


50  PHOTO-ELECTRICITY  [CHAP. 

kinetic  energy  of  the  electron  in  passing  outwards  through  the 
field  of  force.  The  inverse  cube  leads  to  the  result  that  the 
electron  will  have  lost  all  its  energy  when  far  away  from  the 
centre  of  force.  The  system  is  therefore  unsatisfactory.  No  other 
system  in  which  the  law  of  force  is  an  inverse  power  will  give 
us  the  kinetic  energy  at  a  great  distance  from  the  centre  propor- 
tional to  the  frequency  of  the  original  orbit.  Again  no  system  in 
which  the  force  changes  continuously  and  symmetrically  from  the 
centre  outwards  (except  when  it  is  proportional  to  the  distance) 
can  exhibit  resonance  when  the  period  of  the  applied  force  coin- 
cides with  its  natural  period.  The  effect  of  a  wave  of  suitable 
frequency  in  passing  over  a  system  of  this  kind  is  to  cause  the 
electron  to  pass  into  a  new  orbit  whose  period  is  different,  and 
therefore  resonance  ceases.  On  similar  lines,  Herrmann1  has  criti- 
cized atomic  models  described  by  Lindemann  and  others.  It  seems 
clear  therefore  that  no  symmetrical  field  of  force  varying  as  some 
power  of  the  distance  from  the  centre  can  give  results  in  agree- 
ment with  experiment.  The  field  in  an  atom  is  probably  due  to 
several  charges  localized  in  some  definite  order  and  consequently  it 
is  highly  likely  to  be  much  more  complex  than  the  fields  we  have 
been  considering. 

Sir  J.  J.  Thomson2  has  shown  that  the  orbit  of  an  electron 
rotating  on  a  certain  cone  (whose  semi-vertical  angle  is  tan"1  2), 
at  whose  apex  there  is  an  electric  doublet,  is  such  that  the  energy 
is  proportional  to  the  frequency.  If  a  light  wave  of  the  same 
frequency  passes  over  the  system,  the  system  is  disturbed  and  the 
electron  goes  off  with  much  the  same  velocity  as  it  had  in  its  orbit. 
We  must  suppose  that,  at  any  given  time,  only  very  few  atoms 
contain  systems  capable  of  responding  to  light  of  any  particular 
wave-length.  Such  systems  are  not  permanent ;  they  are  probably 
in  a  state  of  continual  change,  dissolving  and  forming  again  with 
different  periods.  Thus  in  a  very  large  assemblage  of  molecules 
there  will  always  be  a  number  in  a  suitable  state  for  ionisation 
by  light. 

It  is  evident  from  our  discussion  that  simple  resonance  systems 
such  as  those  based  on  harmonic  motion  are  not  adequate  to 

1  Herrmann,  Verh.  d.  Deutsch.  Phys.  Ges.  xiv.  p.  936,  1912. 

2  Sir  J.  J.  Thomson,  Phil.  Mag.  xx.  p.  238,  1910. 


Ill]        THE   VELOCITIES   OF   EMISSION   OF   PHOTO-ELECTRONS  51 

account  for  the  results.  We  shall  see  later  that,  if  we  regard  the 
wave  front  as  continuous,  an  electron  vibrating  harmonically  about 
a  centre  of  force  cannot  absorb  sufficient  energy  from  the  light 
waves  to  account  for  its  energy  of  emission.  It  is  therefore 
necessary  to  devise  a  system  in  which  the  energy  of  the  photo- 
electron  is  not  obtained  from  that  of  the  light.  Such  a  system 
would  be  one  in  which  light  of  suitable  frequency  produced  a  state 
of  instability  resulting  in  the  ejection  of  an  electron  with  an 
amount  of  energy  depending  on  the  nature  of  the  system  and  not 
on  the  intensity  of  the  light.  Sir  J.  J.  Thomson's  model  is  of 
this  type  and  moreover  gives  the  correct  relation  between  the 
energy  of  emission  and  the  frequency. 

The  Ionising  Potential  and  Atomic  Volume. 

Experimentally  we  find   that   there   is  a  definite  maximum/ 
wave-length,  characteristic  of  each  substance,  at  which  the  photo-) 
electric  effect  starts.     This  has  been  interpreted  as  indicating  they 
work  necessary  to  take  an  electron  away  from  the  molecule  of  the 
particular  substance.     Table  3  shows  that  the 
work  required  for  ionisation  increases  as  the 
atomic  volume  decreases.     One  can  see  in  a 
general  way  how  this  may  arise.     We  may  con- 
sider the  atom  as  a  positive  charge  localized  at 
the  centre  of  a  sphere  with  the  electron,  having 
an  equal  negative  charge,  on  the  surface.    (The 
positive  charge  is  the   algebraic  sum   of  the 
positive  nucleus  and  the  other  electrons  which 
are  situated  near  the  centre.)     The  potential 
energy  of  the  electron  on  the  surface  is  e?/r, 
where  r  is  the  atomic  radius.     The  potential   energy  therefore 
varies  inversely  as  the  radius  of  the  atom,  or  inversely  as  the 
cube  root  of  the  atomic  volume.     If  we  regard  this  electron  as  the 
photo-electron,  then  a  consideration  of  the  results  for -the  metals 
given  in  Table  3  indicates  that  this  relation  is  roughly  correct  if 
we  keep  to  metals  of  the  same  valency.     For  two  elements  of  the 
same  atomic  volume,  but  different  valencies,  the  potential  energy 
is  greater  in  the  case  of  that  of  the  greater  valency.     This  result 

4—2 


52  PHOTO-ELECTRICITY  [CHAP.   Ill 

may  be  accounted  for  as  follows.  Let  A  represent  a  monovalent, 
and  B  a  divalent  atom.  In  the  divalent  atom  we  picture  two 
electrons  on  the  surface  at  opposite  ends  of  a  diameter,  balanced 
by  a  double  positive  charge  at  the  centre.  The  potential  energy 
of  one  of  the  electrons  in  B  is 


that  is  to  say,  it  is  greater  than  e2/r  for  the  monovalent  atom. 
Similarly  the  potential  energy  between  an  electron  and  the 
trivalent  atom  of  which  it  is  a  part  would  be  greater  than  the 
energy  in  the  case  of  a  divalent  atom  and  so  on. 

This  point  of  view  suggests  that  if  we  plot  the  ionising 
potentials  F0  against  the  atomic  volumes,  and  join  all  the  points 
corresponding  to  elements  of  the  same  column  of  the  periodic 
series,  we  should  get  a  series  of  sloping  lines  one  above  the  other. 
This  is  the  case  when  we  plot  the  results  given  in  Table  3.  So 
little  is  definitely  known  about  the  ionising  potentials  of  the  other 
elements,  or,  what  for  our  purpose  is  the  same  thing,  the  critical 
frequency  at  which  the  photo-electric  effect  begins,  that  it  is 
impossible  to  test  this  view  as  fully  as  one  might  desire.  Certain 
experiments  enable  us  to  form  rough  estimates  of  the  critical 
wave-length  for  a  few  non-metallic  elements.  The  values  for  the 
critical  wave-lengths  lend  some  support  to  the  view  advanced 
above.  An  accurate  knowledge  of  the  critical  wave-lengths  for  the 
different  elements  is  much  to  be  desired. 


CHAPTER  IV 

THE   TOTAL    PHOTO-ELECTRIC   EFFECT 

Influence  of  Gases  on  the  Photo- Electric  Current 

THE  current  obtained  when  light  falls  on  a  plate  whose  potential 
relative  to  the  surrounding  electrode  is  favourable  to  the  escape  of 
negative  electricity,  has  frequently  been  regarded  as  a  measure  of 
the  photo-electric  effect  of  the  plate.  The  results  of  such  experi- 
ments, especially  the  earlier  ones,  are  very  conflicting.  Later  work 
has  shown  that  the  magnitude  of  the  photo-electric  current  is 
affected  to  a  great  extent  by  a  number  of  factors  which,  at  first 
sight,  do  not  seem  to  be  directly  connected  with  the  photo-electric 
action. 

The  total  photo-electric  effect  may  be  defined  as  the  current 
emitted  from  an  illuminated  surface  when  its  potential  is  favour- 
able to  the  escape  of  negative  electricity.  This  chapter  gives  an 
account  of  the  relations  between  the  photo-electric  current  and 
the  factors  on  which  it  depends. 

The  photo-electric  current,  measured  in  the  presence  of  a  gas, 
is  related  to  the  number  of  photo-electrons  set  free  per  second  at 
the  illuminated  surface  in  a  very  complicated  manner.  The  gas 
has  a  two-fold  effect.  (1)  The  number  of  negative  ions  detected 
is  a  function  of  the  nature  of  the  gas  and  its  pressure,  and  the 
potential  difference  between  the  electrodes,  when  the  intensity  of 
the  light,  and  the  number  of  photo-electrons  released,  remains 
constant.  Under  certain  conditions  of  potential,  ionisation  by 
collision  either  in  the  body  of  the  gas,  or  in  the  layer  of  gas 
adjoining  the  surface  of  the  plate,  comes  into  play.  Another 
effect,  that  due  to  the  inertia  of  the  negative  ions  formed  near  the 


54 


PHOTO-ELECTRICITY 


[CHAP. 


illuminated  surface,  has  also  to  be  considered.  (2)  The  gas  may 
actually  reduce  the  number  of  photo-electrons  emitted  from  a  plate 
by  producing  slight  changes  in  the  surface  through  occlusion  or 
chemical  action.  This  phenomenon  will  be  treated  in  the  section 
on  photo-electric  fatigue.  For  purposes  of  discussing  effect  (1), 
we  assume  that  effect  (2)  does  not  come  into  play. 

Fig.  13  gives  the  relation  between  the  photo-electric  current 
and  the  potential  difference  between  the  electrodes  for  different 
pressures1.  The  current  corresponding  to  the  pressure  *008  mm. 


360 


320 


300 


360 


120       180       240 

Potential  in  uo/ts 
Distance  between  electrodes  3'5  mm.  Gas — hydrogen. 

Fig.  13. 

is  independent  of  the  potential  difference  and  represents  the 
number  of  photo-electrons  released.  The  molecules  of  gas  are  too 
few  to  modify  the  amount  of  electricity  escaping  from  the  illumi- 
nated plate.  The  other  curves  however  show  the  great  influence 
of  the  gas  on  the  photo-electric  current.  There  is  no  approach  to 
saturation  when  the  gas  is  at  a  pressure  of  760  mm.  and  the  fields 
are  much  smaller  than  those  necessary  to  produce  ionisation  by 
collision.  The  photo-electrons  emitted  from  the  plate  probably 

1  Varley,  Phil.  Trans.  A.  ecu.  p.  439,  1904. 


IV]  THE   TOTAL   PHOTO-ELECTRIC   EFFECT  55 

stick  to  the  first  neutral  molecules  they  hit,  and  consequently 
they  all  become  negative  ions  very  close  to  the  surface  of  the 
plate.  Now  many  of  these  molecules  are  travelling  towards  the 
plate  and  continue  to  do  so  after  becoming  negative  ions.  Thus 
a  portion  of  the  negative  electricity  is  returned  to  the  plate  and 
the  photo-electric  current  is  less  than  the  number  of  photo-electrons 
emitted.  This  effect  persists  even  when  considerable  fields  are 
applied,  on  account  of  the  inertia  of  those  ions  travelling  towards 
the  plate  and  the  small  distance  they  have  to  go.  To  produce 
saturation,  very  strong  fields  would  be  required ;  but  before  this 
stage  is  reached  ionisation  by  collision  may  set  in.  For  the 
mathematical  theory  of  the  action  described  above,  Sir  J.  J. 
Thomson's  Conduction  of  Electricity  through  Gases,  p.  268  (2nd 
edition),  may  be  consulted. 

When  the  field  is  strong  enough,  ionisation  by  collision 
throughout  the  volume  of  the  gas  will  take  place,  thus  magnifying 
the  current  passing  between  the  two  electrodes.  Since  the  electrons 
are  emitted  with  a  finite  velocity,  a  somewhat  smaller  electric  field 
is  required  to  produce  ionisation  by  collision  in  a  very  thin  layer 
of  gas  adjoining  the  illuminated  electrode  than  in  the  body  of  the 
gas. 

Stole  tow1,  v.  Schweidler2  and  Lenard3  have  investigated  ionisa- 
tion by  collision  when  an  illuminated  plate  acts  as  a  source  of 
electrons.  Consider  two  parallel  plates,  one  of  them  illuminated 
and  at  a  negative  potential  with  respect  to  the  other.  On  keeping 
the  field  constant,  it  is  found  that,  as  the  pressure  increases  from 
zero,  the  photo-electric  current  increases  to  a  maximum  and  then 
diminishes.  Stojetow  found  that  if  the  potential  and  the  distance 
between  the  plates  be  v  and  I  respectively,  then  the  pressure  pm 
at  which  the  current  is  a  maximum  is  given  by  lpm/v  =  const. 
Expressed  in  terms  of  the  electric  force  and  the  mean  free  path  of 
a  molecule  this  becomes  X\  =  const.  Unless  the  potential  differ- 
ence between  the  plates  exceeds  the  ionising  potential,  ionisation 
by  collision  cannot  take  place. 


1  Stoletow,  Jour.  d.  Phys.  n.  (9),  p.  468,  1890. 

2  v.  Schweidler,  Wien.  Ber.  cvin.  p.  273,  1899. 

3  Lenard,  Ann.  d.  Phys.  VHI.  p.  149,  1902. 


56  PHOTO-ELECTRICITY  [CHAP. 

The  theory  of  ionisation  by  collision  as  applied  to  the  photo- 
electric effect  has  been  given  by  Sir  J.  J.  Thomson  (Conduction  of 
Electricity  through  Gases,  p.  271)  and  by  Townsend  (Ionisation  by 
Collision,  pp.  5,  30).  As  the  calculations  are  not  primarily  con- 
cerned with  the  photo-electric  effect,  but  with  a  different  process 
merely  initiated  by  photo-electrons,  only  a  brief  outline  of  the 
theory  will  be  given. 

Let  n0  be  the  number  of  electrons  which  leave  the  illuminated 
plate  and  n  the  number  of  ions  which  arrive  at  the  opposite  plate 
at  a  distance  /.  If  a  be  the  number  of  negative  ions  made  by 
collision  per  cm.,  we  have 

n  =  nQe«l    ...........................  (1), 


where  e  is  the  base  of  the  natural  system  of  logarithms. 

V 

If  —  be  kept  constant,  the  potential  drop  along  the  free  path 

is  unaltered  ;  hence  the  number  of  ions  produced  per  collision  is 
unaltered  too.  (X  is  the  electric  force  between  the  plates,  p  the 
pressure.)  The  number  of  collisions  a  per  cm.  which  result  in  the 
formation  of  another  ion  is  therefore  proportional  to  p  and  hence 
we  have 


The  form   of  the   function  f(X/p)  has  been  determined  by 
Townsend  and  is 

NVp 
Of  X 

-  =  Ne         ...........................  (2), 

P 

where  N  is  the  number  of  collisions  made  by  an  ion  in  passing 
through  1  cm.  of  the  gas  at  1  mm.  pressure,  and  V  the  potential 
fall  along  the  free  path  which  is  necessary  before  an  ion  can  be 
formed  by  collision.  Substituting  for  a  in  (1)  we  have  n  in  terms 
of  these  other  quantities.  Differentiating  with  respect  to  p  it  is 
found  that  n  is  a  maximum  when 


IV] 


THE   TOTAL  PHOTO-ELECTRIC  EFFECT 


57 


which  is  Stoletow's  experimental  relation.     The  maximum  current 
at  pm  is 


Hence  the  ionising  potential  V  in  terms  of  the  maximum  current 
nm,  the  current  in  vacuo  n0,  and  the  potential  difference  v,  is 


Partzsch1  introduces  a  correction  which  makes  the  results  agree 
much  better  with  theory  at  low  voltages.     If  v  be  the  potential 


Photo-electric  current 
r^~*  M  w 

| 

f* 

5 

X 

/ 

\ 

/ 

\ 

^ 

/ 

xo 

-*•  — 

5 

r- 

Pressure  in  mm.  of  Hg 
The  theoretical  curve  shown  in  the  figure  is  for  air. 

v  =  121-5volt;  l  =  -20S  cm.;  *0=-83. 
The  experimental  values  are  indicated  thus  O. 
Fig.  14. 

difference,  and  V  the  ionising  potential,  then  ionisation  by  collision 

(y\ 
1 j .     The  alterations  are 

n.^-H) 

V- v- 


v~v 


1  Partzsch,  Verh.  d.  Deutsch.  Phys.  Ges.  xiv.  p.  60,  1912. 


58  PHOTO-ELECTRICITY  [CHAP. 

The  curve  (Fig.  14)  gives  the  experimental  relation  between  the 
current  and  the  pressure  and  the  corrected  theoretical  relation. 
The  values  of  V,  the  ionising  potential,  obtained  by  Townsend  and 
Partzsch  are  given  in  the  following  table  : 

Partzsch  Townsend 

Air  271  volts  25'0  volts 

N2  27-9    „  27-6    „ 

02  23-9     „ 

H2  27-8     „  26-0    „ 

C02  23-5     „  23-3     „ 

HC1  16-5     „ 

H20  22-4    „ 

A  17-3    „ 

He  14-5     „ 

These  ionising  potentials  are  considerably  larger  than  those 
obtained  by  direct  methods  by  Franck  and  Hertz,  Lenard,  and 
Dember.  Not  only  are  the  magnitudes  different  from  those  given 
by  direct  methods,  but  in  some  cases  the  order  is  reversed  as  may 
be  seen  from  Franck  and  Hertz's  values,  which  are 

He  Ne  Ap  H  0  N 

20-5  16  12  11  9-0  7-5  volts 


Proportionality  between  the  Photo- Electric  Current  and 
the  Light  Intensity. 

Most  theories  of  the  nature  of  ionisation  by  light  lead  to 
definite  relations  between  the  number  of  electrons  emitted  and 
the  intensity  of  the  light.  In  particular,  the  photo-electric  effect 
with  very  weak  light  has  been  investigated,  as  it  is  conceivable 
that,  when  the  intensity  falls  below  a  certain  small  value,  the 
photo-electric  effect  would  diminish  very  rapidly  or  even  perhaps 
cease  altogether.  It  is  known  that  photographic  action  ceases 
when  the  light  intensity  falls  below  a  certain  limit.  If  the  product 
of  the  length  of  exposure  and  the  intensity  of  the  light  be  kept 
constant,  then  the  blackening  of  the  plate,  which  is  constant  over 
a  wide  range,  falls  off  when  the  intensity  is  very  weak.  On  the 
quantum  theory  of  radiation  in  Einstein's  form,  the  energy  in  the 
quantum  is  invariable  and  localized  in  an  element  of  volume  of  un- 
changing size,  and  hence  though  the  whole  energy  in  the  beam  of 


IV]  THE  TOTAL  PHOTO-ELECTRIC  EFFECT  59 

light  may  be  very  small,  one  would  always  expect  a  constancy 
between  the  intensity  of  the  light  (i.e.  the  number  of  quanta)  and 
the  photo-electric  current.  On  certain  resonance  views,  where  the 
energy  is  accumulated  until  it  reaches  the  amount  hn,  it  is  con- 
ceivable that  a  stage  might  be  reached  when  the  accumulation 
from  the  weak  light  is  so  slow,  that  it  never  overcomes  dissipation 
in  other  directions  to  the  extent  necessary  for  the  emission  of  a 
photo-electron. 

Elster  and  Geitel1  first  showed  that  a  proportionality  existed 
between  the  photo-electric  current  from  a  potassium  surface  (in 
vacuo)  and  the  intensity  of  the  light.  Lenard2,  using  a  surface 
covered  with  soot,  showed  that  a  proportionality  existed  over  a  wide 
range.  There  was  a  proportionality  even  when  the  light  intensity 
was  reduced  in  the  ratio  1 : 106  by  reflection  from  a  surface  covered 
with  soot.  There  was  no  indication  of  a  smaller  photo-electric  effect 
with  very  weak  light  than  was  predicted  by  the  proportionality  law. 
Richtmyer3  made  some  very  accurate  measurements,  using  sodium  in 
vacuo  as  his  photo-electric  substance.  He  found  a  strict  proportion- 
ality when  the  intensity  of  the  light  was  varied  from  600  to  *007 
foot  candle  power.  Elster  and  Geitel4  found  that  even  when  the  light 
was  so  weak  that  the  flow  of  energy  was  only  about  10~7  erg  per 
sq.  cm.  per  sec.  and  the  photo-electric  current  about  10~15  amp.,  there 
was  no  evidence  of  any  departure  from  the  proportionality  law. 

Apparent  variations  from   proportionality  can  frequently  be 
accounted  for  by  spurious  effects,  usually  fatigue  or  inverse  fatigue 
effects.    It  seems  quite  conclusive  that  when  disturbing  effects  are  \ 
absent  or  allowed  for,  the  relation  between  the  total  photo-electric  I 
current  and  the  intensity  of  the  light  is  a  linear  one.     The  experi- 
ments of  Griffith5  as  to  the  relation  between  the  photo-electric 
current  and  the  light  intensity  are  not  in  agreement  with  these 
results.    However  the  evidence  is  overwhelmingly  in  favour  of  the 
linear  relation. 

Elster  and  Geitel6  investigated  the  smallest  amount  of  light 

1  Elster  and  Geitel,  Ann.  d.  Phys.  XLVIII.  p.  627,  1893. 

2  Lenard,  Ann.  d.  Phys.  vm.  p.  149,  1902. 

3  Richtmyer,  Phys.  Rev.  xxix.  p.  71,  1909 ;  xxx.  p.  385,  1910. 

4  Elster  and  Geitel,  Phys.  Zeits.  xin.  p.  468,  1912. 

5  Griffith,  Phil.  Mag.  xiv.  p.  297,  1907. 

6  Elster  and  Geitel,  Phys.  Zeits.  xin.  p.  468,  1912. 


60  PHOTO-ELECTKICITY  [CHAP. 

which  would  produce  a  measurable  photo-electric  effect.  For  this 
purpose  they  used  a  very  sensitive  potassium  cell  which  had  been 
treated  by  a  glow  discharge  to  increase  its  sensitiveness  (p.  68). 
The  presence  of  a  small  quantity  of  argon,  in  which  ionisation  by 
collision  could  be  produced,  in  the  cell  enabled  them  to  deal  with 
currents  which  were  100  times  larger  than  the  current  carried  by 
the  photo-electrons  from  the  surface.  The  sensitiveness  of  this 
cell  to  blue  light  was  not  inferior  to  the  human  eye  in  its  most 
sensitive  condition.  It  was  concluded  that  blue  light  imparting 
3  x  10~7  erg  per  sec.  per  sq.  cm.  of  the  potassium  surface  produced 
a  measurable  photo-electric  current  of  5  x  10~13  amp.  The  exposed 
area  of  the  metal  was  12  sq.  cm.  and  the  number  of  electrons 
actually  emitted  from  the  surface  was  magnified  100  times.  Hence 
to  get  the  number  of  electrons  emitted  per  sq.  cm.  we  must  divide 
by  12  x  100.  Thus  the  total  current  carried  away  from  1  sq.  cm. 
of  the  surface  by  the  electrons  is  5  x  10~15  -4- 1200  =  4  x  10~18  amp. 
Since  the  charge  on  an  electron  is  ]_jjfi  v  |fV-M»  coulomb,  this  means 
that  26  electrons  are  emitted  from  1  sq.  cm.  of  the  surface  per 
second.  Taking  hn  as  the  amount  of  energy  associated  with  an 
electron  released  by  light  of  frequency  n,  and  putting 

h  =  6-55  x  10~27,  and  n  =  c/\  =  3  x  1010/(4  x  10~5), 


we  get  the  energy  per  electron  to  beTj^x  10~12j3rgj  Hence  the 
energy  carried  away  by  the  26  photo-electrons  was  1*3  x  10~10  erg. 
But  the  amount  of  energy  supplied  in 'the  beam  of  light  was 
3  x  10~7  erg,  that  is  to  say,  only  2300  times  greater  than  the 
energy  associated  with  the  liberated  photo-electrons.  Two  things 
must  be  remembered.  (1)  Only  a  few  of  the  photo- electrons 
emerge,  the  others  are  absorbed  in  the  surface.  (2)  No  account  is 
taken  of  the  reflected  light,  which  makes  the  amount  of  absorbed 
light  only  a  fraction  of  the  incident  light.  The  ratio  of  the  energy 
of  the  photo-electrons  actually  liberated  in  the  surface  to  that  of  the 
light  absorbed  is  therefore  considerably  less  than  2300.  It  seems 
clear  then  that  we  are  getting  near  to  a  stage  when  the  energy  of 
the  photo-electrons  is  not  much  less  than  that  of  the  incident  light1. 

1  With  reference  to  this  point,  Pohl  and  Pringsheim  (p.  87)  mention  that  a 
potassium  surface  under  certain  conditions  emits  electrons  whose  total  energy 
amounts  to  2o/0  or  3%  of  that  of  the  light  absorbed.  Regarding  the  emerging 


IV]  THE  TOTAL  PHOTO-ELECTRIC  EFFECT  61 

This  has  a  very  important  bearing  on  the  theory  of  the  photo- 
electric effect.  If  the  energy  of  the  electron  is  derived  from  that 
of  the  light  (and  the  wave  fronts  are  continuous),  then  we  should 
expect  the  energy  of  the  photo-electrons  to  be  of  quite  a  different 
order  from  that  of  the  light,  since  we  may  assume  that  the  electron 
absorbs  energy  only  from  a  part  of  the  wave  front  whose  area  is 
comparable  with  the  cross  section  of  a  molecule  or  from  some  still 
smaller  area.  As  experiment  suggests  that  the  energies  are  of 
about  the  same  order,  it  seems  probable  either  that  the  energy  in 
the  wave  front  is  localized  as  in  Einstein's  quantum  theory,  or  that 
the  light  merely  releases  an  electron  with  the  energy  it  had  in 
its  orbit. 

Marx  and  Lichtenecker1  obtained  results  of  the  same  order  as 
Elster  and  Geitel's  for  the  energy  in  the  light  beam  necessary  to 
produce  the  smallest  detectable  photo-electric  current.  In  addition 
to  this,  they  attacked  the  problem  in  another  way.  On  certain 
resonance  theories,  time  is  required  for  the  vibrating  system  to 
acquire  energy  from  the  light  waves.  The  smaller  the  energy  in 
the  light  wave,  the  longer  is  the  time  required.  Hence  it  seemed 
possible  that,  on  illuminating  a  photo-electric  cell  with  weak  light 
for  very  short  periods,  the  photo-electric  current  would  be  smaller 
than  that  calculated  from  the  proportionality  law.  A  very  sensitive 
potassium  cell  was  illuminated  by  the  light  reflected  from  a  re- 
volving mirror.  The  total  amount  of  light  which  fell  on  the  cell 
per  sec.  was  independent  of  the  rate  of  rotation  of  the  mirror, 
and  hence,  if  the  proportionality  law  holds,  the  photo-electric 
current  should  also  be  independent  of  the  rate  of  rotation.  By 
increasing  the  speed  of  the  mirror  the  time  of  illumination  could 
be  cut  down  to  10~7  sec.  during  which  interval  the  surface  was 
receiving  energy  at  the  rate  of  '56  erg  per  sq.  cm.  per  sec.  There 
was  no  departure  from  the  proportionality  law. 

Marx2  calculates  the  maximum  energy  which  an  electron, 
vibrating  under  the  influence  of  a  quasi-elastic  force,  can  acquire 

electrons  as  only  a  fraction  of  the  number  released  in  the  surface,  we  can  safely 
conclude  that  the  energy  of  the  photo-electrons  is  of  the  same  order  as  that  in  the 
incident  light.  Since  the  proportionality  law  is  firmly  established,  these  results 
may  be  taken  as  supporting  the  view  advanced  in  the  discussion  above. 

1  Marx  and  Lichtenecker,  Ann.  d.  Phys.  XLI.  p.  124,  1913. 

2  Marx,  Ann.  d.  Phys.  XLI.  p.  161,  1913. 


62  PHOTO-ELECTRICITY  [CHAP. 

from  a  beam  of  light  with  a  continuous  wave  front.     The  equation 
of  motion  of  such  an  electron  is,  in  Heaviside's  units, 


where  n  is  the  frequency  and  a  the  amplitude  of  the  light  wave, 
c  the  velocity  of  light,  e  the  charge  on  an  electron,  and  fa  the 
quasi-elastic  force  acting  on  the  electron  at  a  distance  x  from  its 
equilibrium  position.  The  second  term  on  the  right-hand  side  is 
the  electric  force  in  the  light  wave  acting  on  the  electron.  The 
third  term  is  the  damping  force  on  the  electron  due  to  the  radia- 
tion which  it  emits  as  its  velocity  changes. 

The  displacement  of  the  electron  at  any  time  is  x  —  bei2rrnt.  On 
substituting  this  in  equation  (3),  and  introducing  the  resonance 
condition /=m(27rn)2,  and  taking  the  real  part,  we  get 

67TC3 

x  =  -.acos(nt--)orx  =  Acos\nt-^ 


(nt  - 1 


The  energy  of  the  vibrating  electron  is 

E=  I    fxdx 
Jo 

9      a?    m    , 

-5-  .  -  C2X4  erg 


where  c/n  =  X.  Now  a2/2  is  the  energy  of  the  light  contained  in 
unit  volume  and  is  equal  to  the  energy  falling  on  unit  area  per 
second  divided  by  the  velocity  of  light.  Thus  when  '56  erg  falls 
on  unit  area  per  second,  as  in  the  experiment  last  described,  the 
energy  density  is  '56/(3  x  1010)  erg  per  c.c.  Substituting  in  (4) 
the  values 

|2  =  3~~xlV  X  =  5x10- cm., 

-  =  1-77  x  107  x  3  x  1010  V4^r,     e  =  4'69  x  10~10  Viir, 
m 

we  get  j£=  1-48  x  10~17  erg. 

This  is  the  greatest  possible  energy  which  an  electron  can 


IV]  THE  TOTAL   PHOTO-ELECTRIC  EFFECT  63 

acquire  from  the  light  wave  when  its  motion  is  represented  by 
equation  (3).  Now  we  know  that  the  energy  of  a  photo-electron 
excited  by  light  of  frequency  n  is  of  the  order  hn,  and  for 
X  =  5  x  10~5  cm.  this  works  out  to  be 

3-3  x  10~12  erg. 

Marx  therefore  concludes  that  the  photo-electron  cannot  possibly 
accumulate  the  necessary  amount  of  energy  from  the  light  wave, 
then  suggests  two  ways  out  of  the  difficulty. 

I.  Assume  that  the  vibrating  electron  does  not  lose  energy  by 
radiation  and  that  therefore  the  equation  of  motion  is  equation  (3) 
without  the  last  term.     Then  it  is  possible  for  the  photo-electron 
to  acquire  the  necessary  amount  of  energy  from  the  light  beam, 
even  when  the  energy  is  distributed  uniformly  over  the  wave  front. 
Such  a  system  introduces  a  good  many  difficulties  and  it  is  doubt- 
ful whether  the  omission  of  the  damping  term  is  any  gain. 

II.  Assume  that  the  light  is  not  distributed  evenly  over  the 
wave  front,  but  that  there  are  places  where  there  is  exceptional 
concentration  of  energy.     The  number  of  photo-electrons  emitted 
gives  the  number  of  concentration  specks  required  and  this  number 
multiplied  by  the  amount  hn  gives  the  total  energy  required  for 
producing  photo-electrons.     This  is  only  about  one  part  in  10,000, 
or   more,   of   the   energy   supplied.     Hence   to   account   for  the 
photo-electric  and  optical  experiments  at  the  same  time,  Marx 
suggests  that   the  wave  surface  may  be  regarded  as  a  number 
of  specks  of  concentrated  energy  distributed  over  a  continuous 
background  and  that  the  total  energy  in  the  specks  need  only  be 
•01%  of  tne  total  energy.     Lorentz1  has  put  forward  a  view  that 
the  amplitude  in  a  light  wave  is  not  uniform  over  the  wave  front 
but  varies  from  place  to  place  according  to  the  law  of  probability. 
There  would  be  very  few  regions  in  which  the  intensity  is  sufficiently 
great  to  communicate  hn  units  of  energy  to  an  electron  according 
to  the  motion  contemplated  in  equation  (3),  and  from  this  it  would 
follow  that  the  total  energy  of  the  photo-electrons  is  small  com- 
pared with  the  energy  in  the  incident  light.     These  regions  of 
great  energy  concentration  correspond  to  the  specks  in  Marx's 

1  Lorentz,  Phys.  Zeits.  xi.  p.  1250,  1910. 


64  PHOTO-ELECTRICITY  [CHAP. 

view.  Marx's  picture  of  a  wave  surface  as  specks  of  intense 
energy  on  a  continuous  background  containing  almost  all  the 
energy  is  built  up  on  the  experiments  in  which  the  total  energy 
of  the  photo-electrons  accounts  for  only  about  '01  °/0  of  the  total 
energy  in  the  incident  light.  The  considerations  we  brought 
forward  on  p.  60,  especially  those  referring  to  Pohl  and  Pring- 
sheim's  experiments,  imply  that,  on  Marx's  view,  the  energy  in  the 
continuous  background  is  only  of  the  same  order  as  that  in  the 
specks.  To  explain  optical  phenomena,  it  seems  necessary  that 
the  energy  in  the  specks  should  be  negligible  in  comparison  with 
that  in  the  continuous  background.  Marx's  dualistic  conception 
of  the  structure  of  the  wave  front,  which  is  only  of  use  when  almost 
all  the  energy  is  localized  in  the  continuous  background,  does  not 
seem  adequate  for  explaining  these  results. 

Applications  to  Radiometry. 

Several  physicists  have  used  photo-electric  cells  for  energy 
measurements  in  radiometry  and  in  doing  so  have  assumed  the 
linear  relation  between  the  photo-electric  current  and  the  light 
intensity.  A  photo-electric  cell  is  in  many  cases  quite  as  convenient 
to  handle  as  a  thermopile  and  a  sensitive  galvanometer,  and  more- 
over enables  one  to  deal  with  light  intensities  of  a  far  smaller 
order  of  magnitude.  A  thermopile  will  detect  a  flow  of  energy  of 
the  order  10"1  erg  per  sq.  cm.  per  sec.,  while  according  to  Elster 
and  Geitel's  work  the  energy  detectable  by  a  photo-electric  cell  is 
10~7  erg  per  sq.  cm.  per  sec.  which  is  comparable  with  the  sensi- 
tiveness of  the  human  eye.  Photo-electric  cells  have  been  used  by 
Nichols  and  Merritt1  for  the  study  of  luminescence,  by  Kichtmyer2 
for  measuring  rapidity  of  photographic  shutters  and  decay  of  phos- 
phorescence, by  Elster  and  Geitel3  for  measuring  light  intensities 
during  solar  and  lunar  eclipses ^  and  by  Harms4  for  studying  the 
changes  of  the  intensities  of  light  during  a  solar  eclipse. 

1  Nichols  and  Merritt,  Phys.  Eev.  xxiv.  p.  471,  1907. 

2  Eichtmyer,  Phys.  Rev.  xxx.  p.  394,  1910. 

3  Elster  and  Geitel,  Phys.  Zeits.  xi.  p.  212,  1910 ;  xin.  p.  582,  1912. 

4  Harms,  Phys.  Zeits.  vn.  p.  585,  1906. 


IV]  THE   TOTAL   PHOTO-ELECTRIC    EFFECT  65 


\/T 


The  Photo- Electric  Effect  and  Temperature. 

The  results  of  the  earlier  experiments  on  the  change  of  photo- 
electric effect  with  temperature  are  very  conflicting.  The  experi- 
ments were  generally  carried  out  in  the  presence  of  a  gas  which 
would  ooze  in  and  out  of  the  surface  of  the  metal  as  the 
temperature  altered.  We  now  know  that  the  amount  of  gas 
occluded  in  the  surface  of  a  metal  has  a  great  influence  on  the 
photo-electric  current  apart  from  temperature  changes.  Zeleny1 
measured  the  photo-electric  effect  of  Pt  and  Fe  in  air  at  different 
temperatures  and  found  it  to  change  with  the  temperature.  The 
change  in  the  photo-electric  effect  lagged  behind  the  change  in 
temperature  which  clearly  indicates  that  the  effect  is  due  to  the 
gas  content  of  the  surface  slowly  adjusting  itself  to  equilibrium  at 
different  temperatures.  Varley  and  Unwin2  found  big  temperature 
changes  in  the  photo-electric  effect  of  Pt  in  different  gases.  In 
hydrogen,  the  effect  increased  rapidly  with  the  temperature, 
in  oxygen  and  CO2  the  effect  decreased  as  the  temperature  rose 
to  about  400°  and  then  started  to  increase.  Final  values  at  any 
temperature  were  only  obtained  after  maintaining  the  Pt  at  that 
temperature  for  a  considerable  time.  Elster  and  Geitel3  found 
that  the  photo-electric  effect  of  potassium  in  the  presence  of 
hydrogen  at  '3  mm.  pressure  increased  50  °/o  as  the  temperature 
changed  from  20°  to  50°.  Sir  J.  J.  Thomson  (Conduction  of  Elec- 
tricity through  Gases,  p.  285)  found  that  when  the  temperature  of 
the  alkali  metals  was  raised  to  about  200°  a  great  increase  in  the 
photo-electric  current  was  obtained. 

On  the  other  hand,  Dember4  investigated  the  effect  in  vacuo 
for  K,  Na,  and  K-Na  alloy  from  room  temperature  up  to  110° 
and  found  no  change  in  the  photo-electric  current.  This  included 
a  change  from  the  solid  to  the  liquid  state  in  the  case  of  K  and 
Na.  Varley  and  Unwin5  repeated  their  experiments  on  the  tem- 
perature effect  of  platinum  in  vacuo  and  found  the  effect  to  be 

1  Zeleny,  Phys.  Rev.  xn.  p.  321,  1901. 

2  Varley  and  Unwin,  Proc.  Roy.  Soc.  Edinburgh,  xxvu.  p.  117,  1907. 

3  Elster  and  Geitel,  Ann.  d.  Phys.  XLVIH.  p.  625,  1893. 

4  Dember,  Ann.  d.  Phys.  xxm.  p.  957,  1907. 

5  Varley  and  Unwin,  Proc.  Roy.  Soc.  Edinburgh,  xxvu.  p.  117,  1907. 
H.  5 


66  PHOTO-ELECTRICITY  [CHAP. 

independent  of  the  temperature  from  60°  to  350°.  Ladenburg1 
found  the  photo-electric  current  from  Pt,  Au  and  Ir  (in  vacuo)  to 
be  independent  of  the  temperature  up  to  800°.  Millikan  and 
Winchester2  found  that  the  photo-electric  current  from  Au,  Ni, 
Ag,  Fe,  Mg,  Sb,  Zn,  and  Pb  in  vacuo  was  independent  of  the  tem- 
perature over  a  range  from  15°  to  125°. 

We  can  conclude  from  these  experiments,  and  those  described  on 
p.  42,  that  the  magnitude  of  the  photo-electric  effect  and  the  velocity 
of  the  photo-electrons  are  alike  independent  of  the  temperature 
of  the  illuminated  plate.     When  there  is  an  apparent  change  with 
the  temperature,  this  may  safely  be  attributed  to  some  secondary  ^ 
effect  of  the  temperature,  such  as  a  change  in  the  amount  of  gas  j 
absorbed,  rather  than  to  the  fundamental  photo-electric  action.       / 

If  the  photo-electrons  were  originally  the  free  electrons  which  / 
take  part  in  electrical  conductivity  and  in  thermionic  effects,  one 
might  expect  that  it  would  be  easier  for  the  light  to  cause  the 
emission  of  the  electrons  at  higher  temperatures.     At  the  higher 
temperatures  there  are  more  electrons  moving  towards  the  surface 
with  velocities  sufficient  to  make  it  an  easy  matter  to  pull  them/ 
through._J  It  is  more  probable  that  the  photo-electron  comes  from 
the  molecule,  in  which  the  forces  tending  to  keep  the  electron^ 
inside  vary  either  very  slowly,  or  not  at  all,  with  the  temperature.  J 

The  Effect  of  an  Electric  Discharge  on  Photo- Electric  Sensitiveness. 

It  is  well  established  now  that  using  a  metal  as  an  electrode  in 
an  electric  discharge  at  low  pressures  alters  the  gas  content  of  the 
surface.  Since  we  know  from  fatigue  and  other  experiments  that 
the  amount  of  occluded  gas  affects  the  photo-electric  sensitiveness 
of  a  metal,  we  should  therefore  expect  that  treating  a  metal  as  an 
electrode  in  a  discharge  would  have  a  marked  effect  on  the  photo- 
electric current  emitted  by  it.  Such  is  the  case.  The  processes 
in  the  discharge  are,  however,  so  complex,  and  so  many  factors 
come  in  to  an  unknown  extent,  that  it  is  not  surprising  that  the 
experimental  results  are  conflicting. 

Holman3  investigated  the  effects  of  using  Zn,  Cu,  Ag,  Al,  and 

1  Ladenburg,  Verh.  d.  Deutsch.  Phys.  Ges.  ix.  p.  165,  1907. 

2  Millikan  and  Winchester,  Phil.  Mag.  xiv.  p.  188,  1907. 

3  Holman,  Phys.  Rev.  xxv.  p.  81,  1907. 


IV]  THE  TOTAL   PHOTO-ELECTRIC   EFFECT  67 

Fe  as  electrodes  in  a  hydrogen  discharge.  After  using  the  metals 
as  cathodes,  the  sensitiveness  increased;  after  using  them  as  anodes, 
the  sensitiveness  decreased,  the  order  of  the  change  being  6  to  1 
in  the  case  of  zinc.  Holman  refers  to  Skinner's  work  in  which 
cathodes  emit  hydrogen  and  anodes  absorb  it.  Holman's  results! 
indicate  therefore  that  the  less  the  amount  of  occluded  hydrogen/ 
the  greater  the  photo-electric  sensitiveness.  Chrisler1  obtained 
quite  different  results  with  a  large  number  of  metals.  The  sensi- 
tiveness was  greater  after  use  as  anode  than  after  use  as  cathode 
in  hydrogen.  When  other  gases  were  used,  he  obtained  the 
reverse  effect,  viz.  a  decrease  in  sensitiveness  after  use  as  anode. 
Consequently  he  suggested  that  if  the  hydrogen  could  be  com-  j 
pletely  removed,  the  photo-electric  effect  might  vanish.  Experi-J 
ments  of  this  kind  are  unsatisfactory  in  that  it  is  extremely  difficult 
to  control  the  various  factors  which  are  introduced  by  the  discharge. 
Skinner's  work  is  quoted  as  indicating  that  a  metal  absorbs 
hydrogen  when  acting  as  anode  in  a  glow  discharge.  But  we  also 
know  that  when  the  pressure  is  sufficiently  low  to  allow  the 
cathode  rays  to  strike  the  anode,  then  hydrogen  and  other  gases  are 
driven  out  of  it.  Thus  slight  differences  in  the  conditions  under 
which  the  discharge  takes  place  may  produce  quite  different  effects 
Both  Holman  and  Chrisler  used  induction  coils,  and  very  probably 
the  discharge  was  not  uni-directional.  A  high  potential  battery 
would  have  avoided  the  possible  trouble  arising  from  reversals. 

Wulf2  found  that  charging  a  sheet  of  platinum  electrolytically 
with  hydrogen  increased  the  photo-electric  current  from  it  about 
ten  times.  A  positively  charged  layer  on  the  surface  of  a  metal 
would  assist,  and  a  negatively  charged  layer  would  retard,  the 
emission  of  photo-electrons.  Such  layers  are  undoubtedly  formed 
on  electrodes  in  discharge  tubes,  and  in  liquids,  as  Wulf 's  result 
indicates.  The  velocity  experiments  with  metals  treated  as  elec- 
trodes support  this  view,  for  after  using  the  metal  as  a  cathode, 
extremely  high  emission  velocities  can  be  obtained. 

We  shall  now  turn  to  certain  changes  produced  by  cathode 
rays  in  the  photo-electric  sensitiveness  of  certain  substances. 

1  Chrisler,  Phys.  Rev.  xxvu.  p.  267,  1908. 

2  Wulf,  Ann.  d.  Phys.  ix.  p.  946,  1902. 

5—2 


68  PHOTO-ELECTRICITY  [CHAP. 

Elster  and  Geitel1  found  that  the  halogen  salts  of  the  alkali  metals 
and  some  other  salts,  such  as  CaCl2,  BaCl2,  K2CO3,  when  coloured 
by  bombardment  with  cathode  rays,  were  extremely  sensitive 
photo-electrically  to  visible  light.  (The  salts  before  colouring  are 
quite  insensitive,  even  to  ultra-violet  light.)  Elster  and  Geitel 
explain  the  colouring  as  being  due  to  free  alkali  metal  dissolved  in 
the  salt,  the  whole  forming  a  solid  solution. 

Later  Elster  and  Geitel2  converted  the  alkali  metals  into 
hydrides  by  heating  them  in  hydrogen  at  a  temperature  of 
about  350°.  The  hydrides  were  in  the  form  of  clear  colourless 
crystals  and  were  quite  insensitive  to  visible  light.  On  bombarding 
the  hydrides  with  cathode  rays,  large  quantities  of  hydrogen  were 
evolved  and  the  hydrides  became  brightly  coloured.  The  colours 
were  blue-violet  for  K,  the  same,  but  paler,  for  Rb,  green  for  Cs, 
and  brown  for  Na.  The  photo-electric  sensitiveness  of  these 
coloured  surfaces  was  from  3  to  4  times  greater  than  that  of  the 
corresponding  pure  metals.  Elster  and  Geitel  regard  these 
coloured  substances  as  the  alkali  metals  in  a  colloidal  state 
dissolved  in  the  solid  hydride.  (The  colouring  is  probably  caused 
in  the  same  way  as  that  of  glasses  stained  with  metallic  oxides.) 
To  get  the  colloidal  modification,  it  is  unnecessary  to  convert  the 
metal  into  the  hydride  as  a  preliminary  step.  The  amount  of 
hydride  can  be  so  small  that  one  may  regard  the  substance  as  a 
pure  colloidal  modification  of  the  metal.  A  glow  discharge  in 
rarefied  hydrogen  in  contact  with  the  ordinary  pure  metal  will 
give  the  colloidal  modification.  Very  small  amounts  of  hydrogen 
will  enable  the  change  from  the  ordinary  form  to  the  colloidal  form 
to  take  place.  To  get  the  greatest  possible  sensitiveness  to  light, 
it  is  necessary  to  leave  a  little  gas  in  the  cell  so  that  the  effect 
may  be  magnified  by  ionisation  by  collision.  In  the  course  of 
time,  however,  the  hydrogen  in  these  cells  containing  the  colloidal 
metals  disappears  and  at  the  same  time  the  colour  fades  and  the 
photo-electric  sensitiveness  falls  off.  The  hydrogen  probably  com- 
bines with  the  colloidal  metal.  This  can  be  avoided  and  a  cell  of 
a  permanent  type  can  be  made  by  substituting  argon  or  helium 
for  the  hydrogen  after  the  colouring  has  been  produced3. 

1  Elster  and  Geitel,  Ann.  d.  Phys.  LIX.  p.  487,  1896. 

2  Elster  and  Geitel,  Phys.  Zeits.  xi.  pp.  257,  1082,  1910. 

3  Elster  and  Geitel,  Phys.  Zeits.  xn.  p.  609,  1911. 


IV]  THE  TOTAL  PHOTO-ELECTRIC   EFFECT  69 

With  a  cell  containing  colloidal  potassium,  Elster  and  Geitel1 
could  detect  the  infra-red  rays  which  passed  through  ebonite 
*97  mm.  thick.  The  effect  apparently  falls  off  gradually  with 
increase  of  the  wave-length,  no  sudden  cessation  being  observed. 

These  cells  are  admirably  adapted  for  detecting  very  weak 
radiation.  The  sensitiveness  is  a  maximum  at  X3200,  X4400, 
X4800  and  (probably)  \5500  for  Na,  K,  Rb  and  Cs  respectively 
(Pohl  and  Pringsheim,  and  Lindemann2).  When  the  best  con- 
ditions for  the  gas  pressure  are  obtained  and  a  suitable  potential 
producing  a  large  amount  of  ionisation  by  collision  is  used,  these 
cells  can  detect  extraordinarily  small  amounts  of  light.  Kemp3 
calculates  that  a  cell  he  used  would  give  a  measurable  current  of 
10~15  amp.  when  illuminated  by  a  candle  at  2'7  miles.  Elster  and 
Geitel4  find  that  their  cells  (of  K)  are  not  inferior  to  the  human 
eye  in  sensitiveness,  especially  in  the  blue  end  of  the  spectrum. 

Pohl  and  Pringsheim5  suggest  that  the  increased  sensitiveness 
of  the  colloidal  modification  is  due  to  the  greater  ease  with  which 
the  electrons  can  emerge  from  the  tiny  globules  of  metal  which 
characterize  the  colloidal  state.  The  average  diameter  of  these 
globules  is  probably  considerably  less  than  10~5cm.  Let  d  (Fig.  15) 
be  the  distance  through  which  the  electron 
can  penetrate.  For  a  smooth  coherent  sur- 
face the  ratio  of  those  which  emerge  to  those 
produced  at  0  is  of  the  order  of  the  solid 


angle  co  to  4?r.     But  if  a  globule  of  radiusN>/ 

d  had  its  centre  at  0,  then  all  the  electrons 

Fig.  15. 

could  emerge.  Bigger  globules  would  be- 
have in  a  way  intermediate  between  the  small  globule  con- 
sidered and  the  flat  surface.  On  these  lines,  Pohl  and  Pringsheim 
account  for  the  greater  sensitiveness  of  a  surface  composed  of  a 
large  number  of  tiny  globules  as  compared  with  ordinary  coherent 
surfaces. 

1  Elster  aud  Geitel,  Phys.  Zeits.  xn.  p.  758,  1911. 

2  Lindemann,  Verh.  d.  Deutsch.  Phys.  Ges.  xin.  p.  482,  1911. 

3  Kemp,  Phys.  Rev.  (2)  i.  p.  273,  1913. 

4  Elster  and  Geitel,  Phys.  Zeits.  xm.  p.  468,  1912. 

5  Pohl  and  Pringsheim,   Verh.  d.  Deutsch.  Phys.  Ges.  xm.  p.  211,  1911;   xv. 
p.  179,  1913. 


70  PHOTO-ELECTRICITY  [CHAP. 


koto-Electric  Fatigue. 


It  has  long  been  known  that  the  photo-electric  sensitiveness  of 
a  recently  exposed  metallic  surface  decreases  with  the  time.  This 
phenomenon  is  called  photo-electric  fatigue.  It  has  been  accounted 
for  in  many  ways,  e.g.  oxidation  of  the  surface,  effect  of  illumination, 
changes  in  the  electrical  double  layer  at  the  surface,  absorption  of 
the  surrounding  gas  by  the  metal,  presence  of  an  electric  field 
assisting  or  retarding  the  photo-electric  current,  and  mechanical 
alteration  of  the  surface.  We  shall  consider  separately  the  fatigue 
in  the  presence  of  a  gas  at  atmospheric  pressure  and  the  fatigue  in 
vacuo. 

Fatigue  in  the  Presence  of  a  Gas. 

Hallwachs1  found  that  the  fatigue  progressed  at  the  same  rate 
whether  the  metal  was  illuminated  or  not.  Neither  did  the  presence^ 
of  an  electric  field,  assisting  or  retarding  the  photo-electric  current,  (^ 
have  any  effect  on  the  rate  of  fatigue.  Illumination  sometimes  * 
appears  to  produce  a  fatigue,  but  this  is  due  to  the  formation  of 
ozone  by  ultra-violet  light  which  is  the  real  cause  of  the  fatigue. 
The  evidence  against  the  oxidation  theory  is  that  the  initial  sensi- 
tiveness and  consequent  fatigue  is  much  the  same  in  Cu,  CuO, 
and  Cu20.  This  also  applies  to  Pb  and  PbO2.  The  photo-electric 
fatigue  of  platinum  was  investigated  simultaneously  with  changes 
in  the  contact  potential.  There  was  no  quantitative  relation 
between  the  two  effects.  Frequently  treatment  which  produced 
strong  fatigue  had  scarcely  any  effect  on  the  contact  potential  and 
vice  versa.  From  this,  Hallwachs  concluded  that  variations  in  the 
electrical  double  layer  were  not  the  cause  of  fatigue.  However, 
the  direction  of  the  change  in  both  phenomena  was  nearly  always 
the  same  (fatigue  and  increase  of  electro-negative  character  usually 
run  together),  and  it  appears  probable  that  both  effects  are  the 
result  of  some  common  cause.  Allen2  supports  Hallwachs  in 
rejecting  these  explanations  of  fatigue. 

Hallwachs  pointed  out  that  the  rate  of  fatigue  is  very  much 

1  Hallwachs,  Ann.  d.  Phys.  xxm.  p.  459,  1907. 

2  Allen,  Proc.  Roy.  Soc.  A.  LXXVIH.  p.  489,  1906  ;  Phil.  Mag.  xx.  p.  564,  1910. 


IV] 


THE   TOTAL   PHOTO-ELECTRIC   EFFECT 


71 


greater  when  the  metal  plate  is  exposed  to  the  free  air  of  a  room 
than  when  it  is  confined  in  a  small  vessel.  A  freshly  cleaned 
copper  plate  fatigued  to  '33  of  its  original  value  in  the  course  of 
a  day  when  exposed  in  a  room.  To  effect  the  same  fatigue  in  a 
closed  vessel,  containing  air  at  atmospheric  pressure,  required 
three  months.  The  open  air  fatigue  is  attributed  to  the  presence 
of  traces  of  ozone  which  produces  a  powerful  fatigue  agent.  The  in- 
troduction of  ozone  into  a  vessel  containing  a  zinc  plate  (Ullmann1), 
and  a  copper  plate  (Hallwachs,  I.e.),  produced  a  very  marked  fatigue, 
which  however  almost  entirely  disappeared  on  removing  the  ozone. 
From  the  temporary  character  of  the  fatigue  it  was  concluded  that 
ozone  does  not  produce  oxidation.  Hallwachs  (Congres  Inter- 
national de  Radiologie,  Brussels,  p.  642,  1910)  suggests  that  the 
fatigue  agent  is  H202  produced  by  ozone  and  moisture.  He  found 
that  H2O2  has  an  enormous  absorption  for  ultra-violet  light  and 
hence  a  very  thin  film  over  the  metal  surface  would  reduce  the 
intensity  of  the  light  very  considerably.  Similar  differences 
between  the  fatigue  in  the  open  air  and  in  a  vessel  have  been 
investigated  by  Allen2. 

The  rate  of  fatigue  of  Cu,  CuO  and  Pt  kept  in  air  in  closed 
vessels  is  given  in  the  following  table  (Hallwachs) : 


Photo-Electric  Sensitiveness 

Time 

Cu 

CuO 

Pt 

0  months 

100 

100 

100 

3        „ 

31 

64 

94 

6       „ 

33 

60 

82 

9       „ 

31 

54 

63 

12       „ 

28 

44 

57 

18       „ 

38 

— 

30       „ 

32 

50 

Hallwachs  attributed  this  fatigue  to  the  slow  absorption  of 
gases  by  the  surface.  The  gases  either  absorb  some  of  the  light 
which  produces  a  photo-electric  effect,  or  retard  the  escape  of 


1  Ullmann,  Ann.  d.  Phys.  xxxn.  p.  1,  1910. 

2  Allen,  Phil.  Mag.  xx.  p.  564,  1910. 


72 


PHOTO-ELECTRICITY 


[CHAP. 


electrons.  This  view  is  supported  by  the  fact  that  the  sensitive- 
ness of  Pt  at  ordinary  temperatures  is  greater  after  being  heated 
and  less  after  being  cooled.  In  the  first  case,  heat  drives  off  some 
of  the  gas  and  hence  the  photo-electric  sensitiveness  is  above  its 
equilibrium  value ;  in  the  second  case,  the  surface  absorbs  more  gas 
and  only  gets  rid  of  it  slowly  at  ordinary  temperatures.  The  most 
reliable  way  of  getting  a  Pt  plate  to  give  constant  initial  values  is 
to  make  it  red-hot.  It  may  be  assumed,  after  such  treatment, 
that  the  occluded  gases  which  give  rise  to  the  fatigue  have  been 
driven  off. 

Ullmann1  found  that  the  fatigue  is  much  more  rapid  with  Zn 
than  with  Cu.  While  the  presence  of  water  vapour  has  but  little 
effect  on  the  fatigue  of  Cu,  it  increases  the  rate  of  fatigue  of  Zn. 
Becker2,  contrary  to  Ullmann,  finds  that  water  vapour  has  the 
power  of  arresting  the  fatigue  which  once  more  proceeds  on 
removal  of  the  water  vapour. 

Allen3  found  for  Zn,  and  Hallwachs  for  Cu  and  Pt,  that  the 
fatigue  was  of  the  same  order  in  hydrogen  as  in  air. 

Ullmann  discovered  that  the  initial  sensitiveness  of  a  plate,  as 
distinct  from  its  fatigue,  depended  largely  on  the  surrounding 
atmosphere.  He  obtained  the  following  values  for  a  zinc  plate. 


Photo-Electric  Sensitiveness 

Atmosphere 

Dielectric 
Capacity 

Dry  gas 

Wet  gas 

H2 

1-00 

2-52 

2-6  xlO-4 

air 

2-94 

8-10 

5-9      „ 

C02 

7'30 

17-40 

9-8      „ 

In  a  recent  paper,  Hallwachs4  puts  forward  the  view  that  there 
is  some  relation  between  the  photo-electric  sensitiveness  and  the 
dielectric  capacity  of  the  gas  in  contact  with  the  surface.  Experi- 
ments with  NH3  support  this  view,  experiments  with  organic 
vapours  are  indecisive.  Hallwachs  now  suggests  that  some 

1  Ullmann,  Ann.  d.  Phys.  xxxn.  p.  1,  1910. 

2  Becker,  Verh.  d.  Deutsch.  Phys.  Ges.  xiv.  p.  806,  1912. 

3  Allen,  Phil.  Mag.  xx.  p.  564,  1910. 

4  Hallwachs,  Verh.  d.  Deutsch.  Phys.  Ges.  xiv.  p.  634,  1912. 


IV]  THE   TOTAL  PHOTO-ELECTRIC   EFFECT  73 

absorption  of  gas  by  a  metal  is  necessary  before  it  will  give  a 
photo-electric  effect  at  all.  If  this  function  is  assigned  to  the 
absorbed  gas,  it  seems  necessary  to  look  elsewhere  for  the  cause  of 
fatigue.  One  cannot  see  from  the  theoretical  standpoint  how  the 
dielectric  capacity  of  the  gas  can  influence  the  photo-electric  effect 
of  the  metal. 

Bergwitz1  showed  that  there  was  no  fatigue  with  cells  contain- 
ing Na,  K,  and  Rb  in  the  presence  of  H2  at  '3  mm.  pressure.  The 
period  of  investigation  never  exceeded  a  few  hours. 

Allen2  found  that  the  photo-electric  effect  of  iron  was  from 
10  to  20  times  less  when  it  was  in  the  "passive"  state  than  when 
in  the  "  active  "  state.  Modern  chemical  research  attributes  the 
"  passivity  "  of  metals  to  the  formation  of  an  imperceptible  surface 
layer  of  oxide  protecting  the  pure  metal  beneath3.  Thus  one 
would  expect  passivity  to  be  accompanied  by  a  great  decrease  in 
the  photo-electric  effect. 

Fatigue  in  vacua.    ~^~ ~~ 

A  number  of  researches  have  been  carried  out  on  the  photo- 
electric fatigue  in  vacuo.  This  term  is  only  justified  when  we  are 
satisfied  that  the  pressure  of  the  residual  gas  is  too  small  to  have 
any  appreciable  effect  on  the  phenomenon  under  investigation. 
That  a  very  small  amount  of  residual  gas  is  sufficient  to  affect  the 
photo-electric  sensitiveness  of  a  plate  is  suggested  by  the  conflict- 
ing results  of  experiments  carried  out  at  low  pressures.  Ladenburg4 
found  that  Al  showed  no  fatigue  in  vacuo  while  Ag  did.  Dember5 
found  that  the  sensitiveness  of  a  Na-K  cell  remained  constant 
for  12  months.  The  Na  cells  used  by  Richtmyer6  showed  no 
fatigue.  Millikan  and  Winchester7  found  there  was  no  fatigue  in 
vacuo  for  the  eleven  metals  tested.  That  fatigue  does  not  occur  in 

1  Bergwitz,  Phys.  Zeits.  vm.  p.  373,  1903. 

2  Allen,  Proc.  Ray.  Soc.  A.  LXXXVIII.  p.  70,  1913. 

3  Grube,  Zeits.  f.  Elektrochemie,  p.  189,  1912;  Isgarischew,  Zeits.  f.  Elektro- 
chemie,  p.  491,  1913. 

4  Ladenburg,  Ann.  d.  Phys.  xn.  p.  538,  1903. 
6  Dember,  Ann.  d.  Phys.  xxni.  p.  957,  1907. 

6  Richtmyer,  Phys.  Eev.  xxx.  p.  394,  1910. 

7  Millikan  and  Winchester,  Phil.  Mag.  xiv.  p.  188,  1907. 


74  PHOTO-ELECTRICITY  [CHAP. 

permanently  sealed  cells  is  supported  by  the  fact  that  such  cells 
are  now  regarded  as  reliable  instruments  for  measuring  light 
intensity. 

On  the  other  hand  a  number  of  investigators  have  observed 
fatigue  in  vacuo.  Allen1  and  Hallwachs  found  fatigue  in  Zn  and 
Cu  respectively.  Robinson2  observed  fatigue  effects  with  Zn  and 
Al.  According  to  his  experiments,  the  fatigue  occurs  only  after 
the  illuminated  plate  has  been  emitting  electrons;  if  they  are 
prevented  from  escaping  by  a  suitable  field,  then  no  change  is 
observed.  Herrmann3  found  that  new  surfaces  of  Ag,  Pt,  Sn,  Pb, 
Al  and  Mg,  exposed  in  vacuo  by  scraping  with  a  steel  tool,  showed 
marked  fatigue.  The  pressure  was  less  than  '0001  mm.  Herrmann 
suggests  that  the  effect  is  due  to  the  formation  of  H202  from  traces 
of  moisture  by  the  ultra-violet  light. 

On  considering  these  investigations  as  to  the  presence  or 
absence  of  fatigue  in  vacuo,  two  well-marked  facts  appear.  In  the 
case  of  the  alkali  metals,  they  are  studied  in  glass  cells  with 
platinum  sealed  electrodes,  so  that  there  is  no  chance  of  any  leak. 
There  is  no  evidence  as  to  how  soon  the  cells  were  tested  after 
being  made.  One  may  presume  that  some  hours  elapsed,  and  so 
it  may  be  considered  that  the  surfaces  had  attained  a  state  of 
equilibrium.  But  it  is  significant  that  in  the  experiments  which 
showed  fatigue,  waxed  joints,  taps,  etc.,  were  essential  parts  of  the 
apparatus,  and  so  there  was  more  chance  of  traces  of  vapours  and 
gases  finding  their  way  into  the  apparatus.  Again,  experiments 
were  usually  carried  out  soon  after  treating  the  surface,  and  hence 
a  re-adjustment  of  the  absorbed  gases  in  the  metal  was  no  doubt 
still  taking  place. 

In  spite  of  the  fact  that  photo-electric  fatigue  has  perhaps  been 
more  investigated  than  any  other  branch  of  photo-electricity,  its 
nature  is  still  obscure.  \  It  seems  clear  that  fatigue  is  connected  in 
some  way  with  the  variations  in  the  amount,  and  the  kinds,  of 
occluded  gases  OT  vapours,  but  as  to  how  these  act  there  is  no 
direct  evidencej  It  does  not  seem  likely  at  present  that  experi- 
ments on  fatigue  will  give  any  information  as  to  the  fundamental 

1  Allen,  Proc.  Eoy.  Soc.  A.  LXXVIII.  p.  489,  1906. 

2  Bobinson,  Phil.  Mag.  xxm.  p.  255,  1912. 

3  Herrmann,  Verh.  d.  Deutsch.  Phys.  Ges.  xiv.  p.  557,  1912. 


IV]  THE  TOTAL   PHOTO-ELECTRIC   EFFECT  75 

processes  of  photo-electricity.  Possibly  when  more  is  known  about 
the  emission^  and  absorption  of  photo-electrons,  experiments  on 
photo-electric  fatigue  will  go  some  way  towards  elucidating  the 
problems  of  absorption  of  gases  by  metals. 

^Photo-Electric  Effect  of  Alloys. 

Euchen  and  Gehloff1  investigated  the  electrical  conductivity  of 
alloys  containing  different  proportions  of  antimony  and  cadmium. 
The  conductivity  of  the  alloys  deviated  in  a  very  marked  manner 
from  that  calculated  on  the  assumption  that  each  metal  contributed 
to  the  conductivity  in  proportion  to  its  amount  in  the  alloy.  The 
result  suggested  to  Herrmann2  the  desirability  of  testing  the  same 
alloys  photo-electrically.  It  was  found  that  the  photo-electric 
effect  of  any  alloy  was  intermediate  between  the  effects  of  the 
constituent  metals  and  varied  linearly  with  the  amount  of  either 
metal  in  the  alloy. 

From  one  point  of  view,  this  result  suggests  that  the  photo- 
electrons  are  not  the  free  electrons  involved  in  electrical  con- 
ductivity. But  one  should  bear  in  mind  that  the  abnormal 
conductivity  of  these  alloys  probably  arises  from  thermo-electric 
effects  between  the  minute  crystals  of  the  different  metals  in  the 
alloy.  (See  Sir  J.  J.  Thomson,  Corpuscular  Theory  of  Matter, 
p.  59.)  So  far  as  the  photo-electric  effect  is  concerned,  each 
crystal  should  give  its  own  effect  characteristic  of  the  metal  and 
thus  the  photo-electric  effect  of  the  alloy  would  be  directly  deter- 
mined by  the  composition  of  the  alloy. 

Some  remarkable  experiments  have  been  published  very  recently 
by  Pohl  and  Pringsheim3  on  the  photo-electric  effect  of  alloys  of 
mercury  and  potassium.  The  results  do  not  agree  at  all  with 
those  given  above.  In  Fig.  16,  the  curve  I  refers  to  the  photo- 
electric effect  of  pure  mercury  while  the  curves  II  to  V  refer  to 
the  alloys.  The  photo-electric  effect  of  the  alloys  is  of  the  same 
order  as  the  normal  effect  for  potassium  and  only  decreases  about 
30  °/0  even  when  the  percentage  of  potassium  changes  from  2*3  to 

1  Euchen  and  Gehloff,  Verh.  d.  Deutsch.  Phys.  Ges.  xiv.  p.  169,  1912. 

2  Herrmann,  Verh.  d.  Deutsch.  Phys.  Ges.  xrv.  p.  573,  1912. 

3  Pohl  and  Pringsheim,  Verh.  d.  Deutsch.  Phys.  Ges.  xv.  p.  431,  1913. 


76 


PHOTO-ELECTRICITY 


[CHAP,  iv 


2  x  10~4,  a  range  of  104  to  1.  The  long  wave-length  limit  of  the 
effect  shifts  only  very  slowly  as  the  amount  of  potassium  decreases. 
One  obvious  difference  between  these  experiments  and  those  of 
Herrmann  is  that  Herrmann's  alloys  were  solid  while  these  are 


A  2000 


Percentage  of  K 


I  0 

II  2x\ 

III  3x10~s 


IV  1-9*10- 

V  2-8 


A  3000 


A  4000 


Fig.  16. 


liquid.  The  results  suggest  that  the  potassium  is  concentrated  in 
the  surface  of  the  alloys,  though  there  are  no  other  grounds  at  all 
for  believing  that  such  is  the  case.  Further  experiments  on  the 
photo-electric  effect  of  alloys  are  required  before  any  adequate 
explanation  can  be  offered. 


CHAPTER  V 


THE  PHOTO-ELECTRIC  EFFECT  AS  A  FUNCTION  OF  THE 
FREQUENCY  AND  STATE  OF  POLARISATION  OF  THE 
LIGHT 

LADENTBURGJ  investigated  the  relation  between  the  photo- 
lectric  effect  and  the  energy  in  the  incident  light  for  different 
,ve-lengths.  He  found  that  the  photo-electric  sensitiveness, 
using  this  term  to  denote  the  photo-electric  current  per  unit 
intensity  of  the  incident  light,  increased  rapidly  with  decreasing 
wave-length  for  Pt,  Cu,  and  Ziv  The  results  for  these  metals 
are  shown  in  Fig.  17.  Similar  results  were  obtained  by  Mohlin2. 
Experiments  have  shown  that 
there  is  a  great  difference  be- 
tween the  alkali  metals  and 
other  metals  in  the  way  in 
which  their  photo-electric  sen- 
sitiveness depends  upon  the 
wave-length  of  the  light.  As 
the  wave-length  decreases,  the 
photo-electric  sensitiveness  of 
each  alkali  metal  reaches  a 
maximum  at  a  particular  wave- 
length and  then  diminishes 
again 


A2600 


A 2200      '     A2400 
Fig.  17. 

The  alkali  metals  possess  still  another  peculiarity;  the 
sensitiveness  depends  very  much  upon  the  state  of  polarisation 
of  the  light. 

In  such  experiments  it  is  necessary  to  have  a  very  smooth 


1  Ladenburg,  Verh.  d.  Deutsch.  Phys.  Ges.  ix.  p.  166,  1907. 

2  Mohlin,  Akad.  Abhandl.  Upsala,  1907. 


78  PHOTO-ELECTRICITY  [CHAP. 

surface,  otherwise  the  plane  of  polarisation  relative  to  the  surface 
will  have  little  meaning.     Failure  to  use  a  sufficiently  smooth 
surface   probably  accounts  partly  for  the   discrepancies   between 
some  of  the  earlier  and  the  later  experiments  on  the  effects  of 
polarisation.      Thus    Ladenburg1    found    that   the    photo-electric 
current  from   polished  steel  did  not  depend  upon  the  state   of 
polarisation  of  the  light.     Elster  and  Geitel2  were  the  first  to 
make  experiments  on  the  variation  of  the  photo-electric  current 
with  the  state  of  polarisation  of  the  light.     A  smooth  surface  was 
furnished  by  the  liquid  alloy  of  sodium  and  potassium,  and  was 
illuminated  by  white  light  striking  the  surface  at  an  angle.     We 
shall  refer  to  the  plane  of  polarisation  parallel  to  the  plane  of 
incidence  as  the  E  JL  plane  and  to  the  plane  of  polarisation  at 
right  angles  to  this  as  the  E\\  plane.     In  terms  of  the  Electro-/ 
magnetic  Theory  of  Light,  E  denotes  the  electric  force  and  the/ 
sign  after  it  denotes  the  relation  of  the   force   to  the  plane  ofl 
incidence.     It  was  found  that  when  the  light  was  polarised  in  thei 
E\\  plane,  the  photo-electric  effect  was  greater  than  when  the  light 
was  polarised  in  the  other  plane.     On  varying  the  obliquity  of  the  \ 
incident  beam,  it  was  found  that  the  photo-electric  current  wasi 
proportional  to  the  amount  of  light  absorbed  when  the  light  was  ' 
polarised  in  the  E  j_  plane ;  but  when  the  light  was  polarised  in 
the  E  ||  plane,  giving  a  much  bigger  photo-electric  current,  the 
current  was  not  proportional  to  the  amount  of  light  absorbed.     If 
however  we  consider  only  the  energy  corresponding  to  the  com- 
ponent of  the  electric  force  at  right  angles  to  the  surface,  then 
there  is  a  proportionality  between  this  part  of  the  energy  absorbed 
and  the  photo-electric  current,  the  small  fraction  of  the  current 
corresponding  to  the  other  component  being  subtracted. 

With  an  angle  of  incidence  of  60°,  the  photo-electric  currents 
from  the  sodium -potassium  alloy  were  as  117  to  2  when  the  light 
was  polarised  in  the  E\\  plane  and  in  the  E  A.  plane  respectively. 

Elster  and  Geitel3  obtained  the  important  experimental  result 
that  the  maximum  emission  velocities  of  photo-electrons  did  not 

1  Ladenburg,  Ann.  d.  Phys.  xii.  p.  558,  1903. 

-  Elster  and  Geitel,  Ann.  d.  Phys.  LII.  p.  433,  1894 ;   LV.  p.  684,  1895 ;   LXI. 
p.  445,  1895. 

3  Elster  and  Geitel,  Phys.  Zeits.  x.  p.  457,  1909. 


V]          EFFECT  OF   POLARISED  AND  MONOCHROMATIC   LIGHT  79 

depend  upon  the  plane  in  which  the  light  was  polarised.  But 
complete  identity  in  the  velocities  was  not  established,  for,  on  the 
whole,  the  electrons  appeared  to  be  slower  when  the  light  was_ 
polarised  in  the  E  ||  plane^  But  for  reasons  similar  to  those  dis- 
cussed on  p.  33,  their  experiments  were  not  adapted  to  obtain 
conclusive  evidence  that  the  distribution  of  velocities  amongst  the 
electrons  emitted  depends  upon  the  state  of  polarisation  of  the 
light.  To  take  an  extreme  case,  suppose  that  light  polarised  in 
the  £\\  plane  causes  the  emission  of  electrons  normally  from . the 
surface,  while  light  polarised  in  the  other  plane  causes  the  electrons 
to  be  emitted  in  all  directions.  Even  if  the  real  distribution  of 
velocities  were  the  same  in  both  cases,  the  apparent  distribution 
of  velocities  given  by  Elster  and  Geitel's  method  would  be 
different. 

Braun1  found  that  K  and  Rb  were  most  sensitive  to  \4400  and 
A,  5 100  respectively. 

Hallwachs2  found,  on  the  other  hand,  that  the  photo-electric 
sensitiveness  of  K  increased  steadily  as  the  wave-length  became 
shorter.  In  Hallwach's  experiments,  the  incidence  was  normal  and 
hence  there  could  be  no  component  of  the  electric  force  in  the 
light  beam  perpendicular  to  the  surface. 

Much  of  the  confusion  in  this  branch  of  photo-electricity  has 
been  cleared  up  by  the  elaborate  and  systematic  investigations  of 
Pohl  and  Pringsheim,  and  now  we  possess  some  very  clear  and 
precise  experimental  information  as  to  the  relation  between  the 
total  photo-electric  current,  the  wave-length  and  the  state  of 
polarisation  of  the  light  for  a  considerable  number  of  metals  and 
some  alloys. 

Pohl3  investigated  the  relation  between  the  photo-electric 
currents  from  surfaces  of  Pt,  Cu,  and  Hg  and  the  state  of  polari- 
sation of  the  light.  To  obtain  metallic  surfaces  of  Pt  and  Cu, 
which  are  so  smooth  that  they  possess  no  irregularities  of  dimen- 
sions comparable  with  the  wave-lengths  used,  thin  films  were 
sputtered  from  suitable  cathodes  on  to  polished  glass  or  quartz 
plates.  In  Fig.  18,  the  relation  between  the  photo-electric  current 

1  Braun,  Dissertation,  Bonn,  1906. 

2  Hallwachs,  Ann.  d.  Phy*.  xxx.  p.  593,  1909. 

3  Pohl,  Verh.  d.  Deutsch.  Phys.  Ges.  x.  pp.  339,  609,  715,  1909. 


80 


PHOTO-ELECTRICITY 


[CHAP. 


and  the  angle  of  incidence  of  the  light  is  given.  When  unpolarised 
light  was  used,  the  dotted  line  was  obtained.  This  is  similar  to 
the  curve  obtained  by  Ladenburg1  which  indicates  that,  in  his 
experiments,  the  surface  was  in  reality  rough  when  considered  in 
relation  to  the  order  of  the  wave-lengths  used,  and  consequently 
the  polarisation  of  the  light  had  little  meaning  relative  to  the 
surface.  The  amount  of  light  absorbed  was  obtained  from  Drude's 
formulae,  and  the  constants  of  Minor  and  Voigt. 


n2  (1  4-  &2)  4-  2n  cos  A/T  4-  cos2  ^ ' 
_  4>n  cos  -\/r 

=  n2  ( 1  +  k2)  cos2  -f  4-  2n  cos  -»|r  +  1 ' 
where  n  is  the  refractive  index,  k  the  absorption  index  and  \jr  the 


Current  per  unit 
intensity  in  incident 
light 


10*     20°     30°     40°     50°     60°     70°     80° 

Angle  of  incidence 
Fig.  18. 

angle  of  incidence.  If  J_L  and  I\\  be  the  respective  photo-electric 
currents,  the  ratios  Ij_/Zj_  and  I  \\JL\\  are  found  to  be  the  same 
for  all  angles  of  incidence.  Hence  it  appears  conclusive  that,  in 
the  case  of  Pt,  Cu,  and  Hg,  the  photo-electric  current  is  propor- 
tional to  the  amount  of  light  absorbed  and  depends  only  upon 
the  state  of  polarisation  of  the  light  to  the  same  degree  as  the 
absorption  does.  The  emission  velocities  of  the  photo-electrons 
were  unaltered  as  the  plane  of  polarisation  was  rotated. 
1  Ladenburg,  Verh.  d.  Deutsch.  Phys.  Ges.  ix.  p.  166,  1907. 


v] 


EFFECT   OF   POLARISED   AND   MONOCHROMATIC   LIGHT 


81 


Pohl  and  Pringsheim  investigated  for  the  alkali  metals  the 
relation  between  the  photo-electric  current  and  the  wave-length 
and  the  state  of  polarisation  of  the  incident  light1.  Their  results 
have  finally  accounted  for  the  contradictory  results  previously 
obtained.  In  Fig.  19,  a  typical  curve  for  Na-K  alloy  illuminated 
obliquely  by  polarised  monochromatic  light  is  given.  Abscissae 
show  the  wave-lengths  and  ordinates  the  photo-electric  current 
per  unit  intensity  in  the  incident  light  beam.  When  the  light 


160 


140 


120 


0  100 


4»  80 
0) 


60 


20 


/ 

\ 

/ 

/ 

/ 

\ 

/ 

\ 

/ 

I*, 

/ 

\ 

4 

o  . 

El 

\ 

\ 

1  —  --^. 

A 

A  3000 


A  5000 


A  6000 


A  4000 

Fig.  19. 
Selective  and  normal  effects  for  Na-K  alloy. 

is  polarised  in  the  E  _L  plane,  the  photo-electric  effect  increases 
rapidly  and  continuously  with  decreasing  wave-length.  When 
however  the  light  is  polarised  in  the  E\\  plane,  a  very  different 
curve  is  obtained.  This  may  be  regarded  as  the  superposition  of 
two  curves,  one  similar  to  the  E  _L  curve  and  the  other  similar  to 
the  curves  of  Fig.  20.  The  former  component  (that  similar  to  the 
E  JL  curve)  can  be  deduced  when  the  proportion  of  the  energy  in 
the  incident  beam  corresponding  to  the  component  of  the  electric 

1  Pohl  and  Pringsheim,  Verh.  d.  Deutsch.  Phys.  Ges.  XH.  p.  215,  1910. 

H.  6 


PHOTO-ELECTRICITY 


[CHAP. 


force  perpendicular  to  the  plane  of  incidence  is  known.  A  maxi- 
mum in  the  curve  does  not  appear  when  the  incidence  is  normal, 
for  then  the  electric  force  in  the  light  has  no  component  perpen- 
dicular to  the  surface,  but  as  the  angle  of  incidence  increases,  this 
peculiarity  in  the  curve  becomes  more  and  more  pronounced.  This 
is  quite  evident  from  Fig.  20  which  gives  the  selective  effects  after 
subtracting  the  normal  effects  for  different  angles  of  incidence1. 

Thus  the  photo-electric  effect  in  the  alkali  metals  may  be 
regarded  (as  by  Pohl  and  Pringsheim)  as  the  superposition  of  two 


280 


A  3000        >i4000       A  5000       A  6000 

Fig.  20. 
Selective  effect  for  Na-K  alloy  with  different  angles  of  incidence. 

distinct  effects,  the  "normal"  effect  and  the  "selective"  effect. 
The  "normal"  photo-electric  effect  increases  with  decreasing  wave- 
length and  does  not  depend  on  the  state  of  polarisation  of  the 
light  except  in  so  far  as  this  affects  the  amount  of  light  absorbed. 
The  "selective"  photo-electric  effect  is  that  part  of  the  total 
photo-electric  effect  which  appears  when  the  light  is  polarised  in 
the  E  ||  plane  and  then  only  over  a  limited  range  of  wave-lengths. 
The  number  of  electrons  liberated  in  the  selective  effect  by  unit 

1  Pohl  and  Pringsheim,  Verh.  d.  Deutsch.  Phys.  Ges.  xii.  p.  682,  1910 


v] 


EFFECT   OF   POLARISED   AND   MONOCHROMATIC   LIGHT 


83 


energy  in  the  light  is  much  greater  than  in  the  normal  effect. 
All  metals  possess  a  normal  effect,  the  selective  effect  has  only 
been  shown  to  exist  for  a  few  metals  mainly  of  the  alkali  group. 

It  is  not  convenient  to  use  polarised  light  except  with  the 
liquid  alloy  of  sodium  and  potassium,  as  it  is  almost  impossible 
to  get  surfaces  of  the  solid  alkali  metals  of  sufficient  smoothness. 
This  does  not  cause  much  trouble,  however,  for  the  effect  can  be 
studied  with  unpolarised  light.  The  selective  effect  is  so  marked 
that  it  shows  up  well  on  the  curve.  The  curve  for  rubidium  with 
unpolarised  light  is  given  in  Fig.  21.  (In  view  of  later  experiments 
(p.  86)  by  Pohl  and  Pringsheim  it  is  well  to  note  that  the  presence 


23 


24 


o 

le 


\ 


A300O  A  4000  A  5000 

Fig.   21. 
Rubidium.     Normal  and  selective  photo-electric  effects  superposed. 

of  a  maximum  in  the  curve  is  not  in  itself  sufficient  to  show  the 
existence  of  a  selective  effect.)  The  position  of  Xmax.,  the  wave- 
length at  which  the  selective  effect  is  a  maximum,  shifts  towards 
the  ultra-violet  as  the  atomic  weight  of  the  alkali  metals  decreases. 
At  the  same  time,  the  magnitude  of  the  selective  effect  becomes 
less  and  the  curve  representing  it  becomes  broader.  The  following 
table  gives  a  summary  of  the  positions  and  breadths  of  the  selective 
regions  for  some  metals  and  alloys1. 

1  Pohl  and  Pringsheim,  Verh.  d.  Deutsch.  Phys.  Gts.  xi.  p.  1039,  1910. 

6—2 


84 


PHOTO-ELECTKICITY 


[CHAP. 


Metal 

A  max. 

Breadth  of  the 
selective  region 

Rb 

4700 

1800 

K 

4400 

2500 

K-Na  alloy 

3900 

2900 

K-Hg  alloy 

Na 

3800 
3400 

2900 
£13200 

K-T1  alloy 

3000 

>3200 

Li 

2800 

_ 

Ba 

2800 

— 

While  the  position  of  Xmax  remains  constant  for  any  one  metal, 
the  ratio  of  the  selective  effect  to  the  normal  effect  varies  enor- 
mously in  different  cells  containing  the  same  metal.  With  one 
cell  (Na-K  alloy),  the  selective  effect  was  300  times  the  normal 
effect,  and  frequently  ratios  of  10  or  15  to  1  were  obtained.  A  cell 
used  by  Elster  and  Geitel  gave  a  ratio  of  50  to  1.  The  angle  of 
incidence  was  always  60°. 

When  potassium  was  made  into  an  alloy  by  the  addition  of 
other  metals,  there  was  a  marked  change  in  the  selective  effect 
and  in  many  cases  it  disappeared1.  The  alloy  which  was  investi- 
gated in  most  detail  was  that  of  potassium  and  mercury.  It 
appears  that  the  act  of  adding  mercury  to  potassium  is,  first  to 
reduce  the  selective  effect  and  to  shift  it  towards  the  ultra-violet, 
while  the  normal  effect  ends  at  about  the  same  wave-length,  and 
then  when  the  selective  effect  has  disappeared,  to  shift  the  limit 
of  the  normal  effect  towards  the  ultra-violet. 

Pohl  and  Pringsheim  also  investigated  alloys  of  potassium  with 
other  elements2.  The  alloys  examined  were  those  with  Bi,  Sb, 
and  P,  and  those  with  Bi,  Pb,  Tl,  and  Hg.  The  first  three  belong 
to  the  same  column  of  the  periodic  series  and  the  other  four  to 
the  same  horizontal  row.  Only  alloys  with  Tl  and  Hg  showed  any 
trace  of  a  selective  effect,  the  maxima  being  at  X3000  and  X.3800 
respectively.  The  long  wave-length  limit  of  the  normal  effect  was 
more  or  less  displaced  in  the  case  of  the  other  alloys.  The  ap- 
proximate limits  for  the  Bi,  Pb,  Sb,  and  P  alloys  were  X4600, 


1  Pohl  and  Pringsheim,  Verli.  d.  Deutsch.  Phys.  Ges.  xn.  p.  697,  1910. 

2  Ibid.  xii.  p.  1039,  1910. 


v] 


EFFECT  OF   POLARISED   AND   MONOCHROMATIC   LIGHT 


85 


A  4400,  \4000  and  A  3600  respectively.  We  may  summarize  these 
results  by  saying  that  the  photo-electric  effect  of  an  alloy  con- 
taining potassium  differs  more  from  the  photo-electric  effect  of 
pure  potassium,  the  more  electro-negative  is  the  other  component. 
Pohl  and  Pringsheim1  found  that  there  was  no  evidence  of  a 
selective  photo-electric  effect  for  Tl,  Pb,  Sn,  Cd,  and  Bi,  and  of 
course  one  may  infer  the  same  conclusion  for  Sb  and  P  mentioned 
above.  Some  interesting  results  were  obtained  for  the  normal 
effect.  Since  all  the  metallic  surfaces  were  prepared  in  vacuo, 
the  results  for  different  metals  are  more  comparable  with  each 
other  than  is  usually  the  case.  The  results  given  in  the  paper 
are  here  put  into  different  units  in  order  to  bring  out  the  fact 
that  the  variation  of  the  photo-electric  effect  from  one  wave- 
length to  another  is  much  the  same  for  the  metals  which  show 
no  selective  effect. 


Wave- 
length 

Photo-ejectric  current  per  unit  incident  energy 

Tl 

Pb 

Sn 

Cd 

Bi 

3650 
3130 
2540 
2300 

<1 
5-8 
62-1 
100 

<1 

re 

50-4 
100 

<1 
1-4 
55-2 
100 

0 

<1 

59-2 
100 

0 
<1 
56-3 
100 

As  may  be  seen,  the  differences  of  the  effects  for  A  2300  and 
A  2540  are  approximately  the  same  for  all  metals  and  this  also 
holds  for  A2540  and  A3130. 

On  investigating  the  photo-electric  effect  of  calcium  in  the 
same  way,  results  were  obtained  from  which  it  might  be  con- 
cluded that  calcium  has  a  selective  effect  with  a  maximum  near 
A35002.  Further  experiments  showed  that  this  was  not  the  case. 
As  the  angle  of  incidence  of  the  light  on  the  calcium  surface  was 
increased,  the  curves  changed  as  shown  in  Fig.  22.  We  see  that 
when  the  angle  of  incidence  is  70°,  the  part  which  is  like  a 
selective  effect  has  disappeared  entirely.  The  real  selective  effect? 
on  the  other  hand,  as  obtained  with  Na-K  alloy,  Fig.  20,  becomes 

1  Pohl  and  Pringsheim,  Verh.  d.  Deutsch.  Phys.  Ges.  xrn.  p.  474,  1911. 

2  Ibid.  xv.  p.  Ill,  1913. 


PHOTO-ELECTRICITY 


[CHAP. 


more  and  more  marked  as  the  angle  of  incidence  is  increased.  The 
authors  explain  the  effect  in  calcium  as  being  due  to  the  greater 
penetrating  powers  of  the  shorter  waves,  and  consequently 
fewer  of  the  photo-electrons  produced  by  the  shorter  waves 
emerge  as  compared  with  those  produced  by  the  longer  waves. 
When  the  incidence  is  oblique,  the  absorption  of  light  takes 
place  in  a  thinner  layer  of  the  surface ;  and  the  electrons,  whether 


rg 


un 
ht 


c  curren 
inciden 


00 

30 
25 

20 
15 
10 

X20 

\ 

V 

x 

\s 

X 

•>- 

_\, 

s; 

\ 

V 

nr\ 

\ 

X^ 

, 

N^A. 

i 

00                                A  3000                                A  4000 

Fig.  22.     Calcium. 
Angle  of  incidence 
I  0°, 
II  45°, 
III  70°. 

produced  by  the  light  of  longer  or  of  shorter  wave-lengths,  have 
more  equal  chances  of  emerging.  Thus  a  maximum  in  the  curve 
does  not  of  itself  prove  that  a  metal  has  a  real  selective  effect. 
It  is  necessary  either  to  show  that  it  is  produced  only  by  light 
polarised  in  the  E\\  plane,  or  else  that  the  effect  becomes  more 
marked  with  increasing  incidence.  Hence  further  experiments  are 
required  to  decide  whether  the  maxima  obtained  for  Ba  and  for 
K-Hg  alloys  indicate  real  selective  effects. 

All  the  results  above  relate  to  the  photo-electric  effect  in  terms 
of  the  energy  of  the  incident  light.     Lately  Pohl  and  Pringsheim1 
1  Pohl  and  Pringsheim,  Verh.  d.  Deutsch.  Phys.  Ges.  xv.  p.  173,  1913. 


v] 


EFFECT   OF   POLARISED   AXD   MONOCHROMATIC   LIGHT 


87 


have,  by  an  ingenious  method,  measured  the  photo-electric  effect 
in  terms  of  the  energy  absorbed  from  the  beam  of  light.  This  is 
a  great  improvement  and  makes  for  precision  in  interpreting  the 
results  of  the  experiments.  In  Fig.  23  we  have  two  curves,  one 
giving  the  photo-electric  effect  for  potassium  per  unit  intensity  of 
the  incident  light,  and  the  other  the  photo-electric  effect  per  unit 
intensity  of  the  absorbed  light.  It  is  quite  evident  from  the  curves 
that  the  region  in  which  the  selective  effect  appears  is  a  region  of 
exceptionally  high  reflecting  power. 

The  selective  effect  stands  out  still  more  clearly  when  the 
colloidal  modifications  of  the  alkali  metals  are  investigated1.     In 


50 

to 

\" 

Q 

.g30 


20 


A  3000  A  4000          A  5000          A  6000 

Fig.  23.    Potassium. 
A  refers  to  incident  light.         B  refers  to  absorbed  light. 

this  case  the  total  energy  of  the  photo-electrons  emitted  in  the 
selective  region  is  as  high  as  2  °/0  to  3  °/o  of  the  energy  in  the 
absorbed  light. 

Theoretical  Considerations  as  to  the  Selective  Effect. 

No  satisfactory  explanation  of  the  selective  effect  is  yet  avail- 
able. Pohl  and  Pringsheim  have  suggested  that  it  is  a  molecular 
resonance  phenomenon  in  which  the  electron  follows  the  electric 
force,  and  thus  the  much  greater  number  of  electrons  which 
emerge  when  the  electric  force  has  a  component  normal  to  the 
surface  is  accounted  for.  The  form  of  the  curve  for  the  selective 
effect  strongly  suggests  some  kind  of  resonance.  Presumably,  on 
this  view,  all  the  systems  concerned  have  the  same  period  which 


1  Pohl  and  Pringsheim,  Verh.  d.  Deutsch.  Phys.  Ges.  xv.  p.  173,  1913. 


88  PHOTO-ELECTRICITY  [CHAP. 

corresponds  to  Xmax .  But  the  great  width  of  the  curve  for  the 
selective  effect — about  an  octave — implies  strong  damping  of  the 
motion  of  the  electron  involved,  far  greater  than  occurs  in  the 
systems  usually  considered.  If  the  systems  concerned  have  a 
natural  period  corresponding  to  Xmax ,  then  we  should  expect 
rather  more  electrons  to  be  emitted  near  this  wave-length  even 
when  the  light  is  polarised  in  the  E  _L  plane.  For  if  the  electrons 
are  now  ejected  from  their  systems  parallel  to  and  in  the  surface, 
then  a  certain  proportion  may  be  scattered  outwards,  and  we 
should  expect  more  of  these  to  emerge  from  the  surface  when 
illuminated  by  light  of  the  wave-length  Xmax  as  more  systems  lose 
electrons  under  this  condition.  This  is  not  the  case.  The  difficulty 
can  be  avoided  by  assuming,  as  Lindemann1  has  done,  that  the 
systems  concerned  only  allow  the  electron  to  vibrate  normally  to 
the  surface.  This  seems  rather  an  artificial  conception,  and  more- 
over it  has  been  pointed  out  before  that  the  energy  of  an  electron 
ejected  from  a  linear  system  should  depend  on  the  intensity  of  the 
light. 

A  knowledge  both  of  the  distribution  of  velocities  amongst  the 
electrons  emitted  in  the  selective  effect  and  also  of  their  directions 
of  emergence  would  be  necessary  for  proper  discussion  of  this 
question.  It  seems  fairly  evident,  however,  from  Elster  and 
GeiteFs  experiment  (p.  78)  that  the  velocities  of  the  photo- 
electrons  are  much  the  same  whether  they  are  emitted  in  the 
selective  or  in  the  normal  effects.  It  seems  likely  therefore  that 
both  sets  of  electrons  originate  in  the  same  kind  of  system  and 
therefore  the  introduction  of  a  special  kind  of  resonant  system  to 
account  for  the  selective  effect  is  unnecessary.  To  account  then 
for  the  much  greater  number  of  electrons  emitted  with  light  of 
certain  wave-lengths  polarised  in  the  E  \\  plane,  it  seems  necessary 
to  attribute  the  effect  to  some  singularity  in  the  optical  properties 
of  the  surface.  Very  little  is  known  about  the  optical  properties  of 
the  alkali  metals,  the  only  investigations  giving  the  optical  con- 
stants of  sodium  and  potassium  being  those  of  Duncan2  which 
unfortunately  do  not  extend  as  far  as  Xmax  for  these  metals.  But 
Pohl  and  Pringsheim  have  made  the  important  observation  that 

1  Lindemann,  Verh.  d.  Deutsch.  Phys.  Ges.  xm.  p.  482,  1911. 

2  Duncan,  Phys.  Rev.  (2)  i.  p.  294,  1913. 


V]          EFFECT  OF   POLARISED   AND   MONOCHROMATIC   LIGHT  89 

the  selective  region  is  also  a  region  of  high  reflecting  power./ 
Consequently,  according  to  optical  theory,  the  part  of  the  light 
which  goes  into  the  surface  is  very  quickly  absorbed,  and  the 
photo-electrons  corresponding  to  this  region  have  a  much  greater 
chance  of  emerging  as  they  are  released  nearer  the  surface  than 
the  others.  It  would  be  interesting  to  see  whether  the  high 
reflecting  power  of  the  surface  in  this  region  is  confined  to  light 
polarised  in  the  E  \\  plane,  or  whether  it  is  shared  by  light 
polarised  in  the  E  j_  plane  as  well.  It  should  be  mentioned  that 
the  ordinary  optical  theory  of  metals  does  not  indicate  that  the 
rate  of  absorption  of  light  should  depend  on  the  state  of  polarisa- 
tion. But  Quincke1  has  shown  that  the  penetrating  power  of  the 
light  depends,  to  some  extent,  on  its  plane  of  polarisation.  The 
possibility  that  the  selective  effect  is  in  some  way  related  to  the 
optical  properties  of  the  surface  is  perhaps  not  wholly  without 
foundation.  The  wave-length  at  which  the  selective  effect  is  a 
maximum  does  not  seem  to  be  connected  with  any  of  the  known 
optical  properties  of  the  metals.  All  that  we  can  say  is,  that  the 
selective  maxima  shift  towards  the  red  as  we  pass  from  Li  to  Cs 
and  a  similar  relation 'holds  for  the  "convergence  frequency"  of 
the  principal  spectral  series  for  the  same  metals. 

To  identify,  as  we  have  suggested,  the  selective  and  normal 
effects  as  fundamentally  the  same  process  is,  perhaps,  simplifying 
the  conception  of  the  photo-electric  effect  at  the  expense  of  the 
optical  theory.  But  little  is  known  about  the  optical  properties 
of  the  alkali  metals  and  the  experimental  result  that  the  velocities 
of  the  photo-electrons  are  of  the  same  order,  whether  produced  in 
the  selective  or  in  the  normal  effect,  is  a  very  strong  argument 
in  favour  of  regarding  the  effects,  from  the  photo-electric  point  of 
view,  as  fundamentally  identical. 


Sensitiveness  of  Aluminium,  Magnesium  and  Calcium. 

Pohl  and  Pringsheim  described  some  remarkable  experiments 
on  the  photo-electric  effects  of  distilled  aluminium,  magnesium  and 
calcium  in  which  there  was  a  great  change  of  sensitiveness  within 

1  Quincke,  Pogg.  Ann.  cxxn.  p.  177,  1866. 


90 


PHOTO-ELECTRICITY 


[CHAP. 


a  few  hours  after  the  surface  had  been  formed1.  The  metals  were 
distilled  in  a  very  good  vacuum  and  the  photo-electric  sensitiveness 
of  the  distilled  portion  was  measured  at  intervals.  Some  curves 
for  magnesium  are  produced  in  Fig.  24  and  they  are  typical  of  the 
curves  for  the  other  two  metals.  The  sensitiveness  increases  very 
appreciably  in  the  course  of  a  day  and  after  a  time  a  maximum 
appears  in  the  curves.  A  still  more  remarkable  effect  is  the  growth  of 
sensitiveness  in  the  visible  part  of  the  spectrum  and  even  in  the  infra- 
red. These  results  are  difficult  to  reconcile  with  those  of  Richardson 


Magnesium 
Age  of  Surface 


•    few  minutes 
x    £:  20  min 
O    £=    Jhour 
O ^    5  hours 


Q     =G:   24  hours 


A  3000 


A  4000 


Fig.  24. 


and  Compton  and  the  writer.  Applying  the  formula  V  =  kn  —  V0  to 
these  results  indicates  that,  if  the  photo-electric  effect  extends  to 
X7000,  F0  has  a  value  as  small  as  1*5  volts.  If  this  interpretation 
is  correct,  one  would  expect  these  metals  to  emit  thermionic  currents 
at  quite  low  temperatures.  The  appearance  of  a  maximum  on  the 
curve  does  not  indicate  the  presence  of  a  selective  effect.  In  the 
case  of  calcium,  it  was  shown  that  the  maximum  disappeared  at 
oblique  incidences  and  one  may  presume  the  same  to  be  the  case  for 

1  Pohl  and  Pringsheim,  Verh.  d.  Deutsch.  Phys.  Ges.  xiv.  p.   546,  1912;  xv. 
p.  Ill,  1913. 


V]          EFFECT  OF   POLARISED   AND   MONOCHROMATIC  LIGHT  91 

magnesium  and  for  aluminium.  One  may  possibly  explain  the 
change  in  sensitiveness  in  this  way.  Immediately  after  distillation, 
the  surface  layers  are,  like  the  interior,  amorphous  in  structure,  but 
after  a  time  a  definite  structure  is  formed  in  the  surface.  The 
change  from  the  amorphous  state  to  the  more  permanent  state  will 
very  likely  be  accompanied  by  changes  in  the  absorbing  power  of 
the  substance  both  for  electrons  and  for  light.  It  is  also  possible 
that  some  re-adjustment  of  the  occluded  gases  in  the  recently  formed 
surface  layers  takes  place  and  that  the  change  of  sensitiveness  with 
the  time  is  associated  with  this.  This  of  course  does  not  explain 
why  the  sensitiveness  to  the  red  and  infra-red  makes  its  appearance. 


CHAPTER  VI 


^PHOTO-ELECTRIC   PROPERTIES    OF   THIN    METALLIC   FILMS 

RONTGEN  rays  and  7-rays  on  passing  through  thin  films  are 
known  to  produce  different  ionisation  effects  on  the  two  sides. 
The  number  of  electrons  and  of  secondary  rays  is  greater  on  the 
side  from  which  the  main  beam  emerges.  On  the  other  hand,  the 
velocities  of  the  electrons  emitted  on  both  sides  of  a  thin  sheet  of 
metal  struck  by  X-rays  appear  to  be  the  same  (Beatty1).  Similar 
asymmetric  effects  have  been  observed  with  the  photo-electrons 
emitted  on  the  two  sides  of  a  thin  film.  From  general  considera- 
tions, one  might  expect  rather  more  electrons  to  emerge  in  the 
direction  in  which  the  light  is  travelling,  on  account  of  the 
momentum  which  the  light  imparts  to  the  electrons  in  that 
direction.  Closer  investigation  however  shows  that  the  momentum 
imparted  is  much  too  small  to  account  for  the  effects  observed. 
We  shall  refer  to  the  side  of  a  thin  film  on  which  the  light  falls 
as  the  incident  side,  and  to  the  other  side  as  the  emergent  side. 
There  are  two  distinct  effects  to  be  investigated,  the  asymmetry 
in  the  number  of  the  photo-electrons  emitted  on  the  two  sides, 
and  the  asymmetry  in  their  velocities.  Of  the  two,  the  latter  is 
perhaps  the  more  difficult  to  investigate  successfully.  * 

The  films  necessary  for  these  experiments  have  to  be  so  thin 
(semi-transparent)  that  they  must  be  supported  in  some  way. 
They  are  produced  by  placing  a  quartz  plate  below  the  cathode 
in  a  discharge  tube  and  passing  the  discharge  until  a  layer  of  the 
metal  of  suitable  thickness  is  sputtered  on  to  the  plate  from  the 
cathode. 

1  Beatty,  Phil.  Mag.  xx.  p.  320,  1910. 


CH.  VI]     PHOTO-ELECTRIC  PROPERTIES  OF  THIN  METALLIC  FILMS    93 


Asymmetry  in  the  Numbers  of  Photo- Electrons  emitted 
from  the  two  Sides  of  a  thin  Film. 

Kleeman1  found  that  the  ionisation  produced  in  air  was  15  °/0 
greater  on  the  emergent  side  of  a  thin  platinum  film  than  on  the 
incident  side.  If  the  photo-electrons  emitted  on  both  sides  have 
the  same  distribution  of  velocities,  then  the  ionisation  produced  is 
proportional  to  the  number  of  electrons  emitted.  Kleeman  also 
found  that  17  °/o  more  electrons  were  emitted  on  the  emergent 
side  of  the  platinum  film  in  vacuo  than  on  the  incident  side. 

Stuhlmann2  measured  the  photo-electric  effect  on  the  two  sides 
of  a  platinum  film  in  air  and  found  17  %  excess  on  the  emergent 
side.  The  following  table  contains  the  results  of  similar  experi- 
ments on  other  metals. 


Period 

Metal 

Eatio  emergent  effect 

-    Eatio     -xlO* 

incident  effect 

Atomic  Weight 

, 
II 

Mg 

1-06 

435 

III 

Fe 

1-02 

182 

IV 

jCu 
iZn 

1-08 
I'll 

170 
170 

VI 

(Ag 
(Sn 

1-07 
1-15 

99 
97 

VII 

Pt 

1-17 

60 

IX 

Pb 

1-12 

54 

Stuhlmann  pointed  out  that  the  ratio  of  the  emergent  to  the 
incident  effect,  divided  by  the  atomic  weight,  is  constant  for 
elements  of  the  same  period  (or  row)  in  the  periodic  table.  The 
quotient  decreases  consistently  as  we  pass  from  one  period  to  the 
next.  No  explanation  for  this  law  is  suggested.  It  is  unfortunate 
that  the  number  of  elements  which  can  be  tested  for  this  effect  is 
restricted  on  account  of  the  great  difficulty  of  sputtering  uniform 
layers  of  most  of  the  other  elements. 


1  Kleeman,  Proc.  Roy.  Soc.  A.  LXXXIV.  p.  92,  1910. 

2  Stuhlmann,  Phil.  Mag.  xx.  p.  331,  1910;  xxn.  p.  854,  1911. 


94  PHOTO-ELECTRICITY  [CHAP. 

From  the  recent  work  of  Partzsch  and  Hallwachs1,  it  now  seems 
very  doubtful  whether  the  above-mentioned  results  imply  any 
asymmetry  at  all  in  the  photo-electric  effect  on  the  two  sides  of  a 
thin  film.  The  asymmetry  seems  to  arise  from  the  different  amounts 
of  light  absorbed  by  the  film,  according  as  the  light  enters  from  the 
air  side,  or  from  the  quartz  side.  If  Eq  is  the  amount  of  light 
penetrating  the  film  when  the  light  is  incident  on  the  quartz  side, 
and  Ea  the  amount  when  the  light  comes  from  the  air  side,  then 


Ea  V+^+^ 

where  nq  is  the  refractive  index  of  quartz,  and  n  and  k  the  optical 
constants  for  the  metal  forming  the  film.  This  ratio,  calculated 
for  X2570,  is  for  the  following  metals  : 

Fe  Ag  Cu          Pt 

1-015         1-125         1-13         1-14 

Stuhlmann's  values  for  the  asymmetry  in  the  photo-electric  effect 

are  : 

Fe  Ag  Cu  Pt 

1-02  1-07  1-08         1-17 

It  seems  that  here  we  have  the  clue  to  the  explanation  of  the 
asymmetry,  viz.  that  it  depends  on  the  different  amounts  of  light 
absorbed,  according  to  the  direction  of  the  incident  light.  The 
formula  above  does  not  take  into  account  multiple  reflections. 
The  authors  then  investigated  by  direct  experiment  the  absorption 
of  light  by  platinum  films  on  quartz.  They  found  that  when  a 
beam  of  light  was  incident  from  the  quartz  side  40  °/o  more  light 
was  absorbed  in  the  film  than  when  the  beam  was  incident  on  the 
air  side  of  the  film.  In  view  of  this  ratio,  it  cannot  be  maintained 
that  it  has  been  shown  that  any  asymmetry  exists  in  the  number 
of  photo-electrons  emitted  from  a  thin  film  when  equal  amounts 
of  light  are  absorbed. 

Partzsch  and  Hallwachs  conclude  that  99  °/o  of  the  photo- 
electrons  emerge  from  a  layer  thinner  than  28  x  10~7cm.  and  that 
only  1  °/0  of  the  light  penetrates  beyond  78  x  10~7  cm.  It  would 
be  very  desirable  to  investigate  this  matter  again  with  light  of 
different  wave-lengths.  It  is  probable  that  the  penetrating  power 
of  the  photo-electrons  would  increase  with  their  velocity. 
1  Partzsch  and  Hallwachs,  Ann.  d.  Phys.  XLI.  p.  247,  1913. 


VI]      PHOTO-ELECTRIC   PROPERTIES  OF  THIN   METALLIC  FILMS       95 

Asymmetry  in  the  Velocities  of  Photo- Electrons  emitted 
from  the  two  Sides  of  a  thin  Film. 

The  velocities  of  the  photo-electrons  emitted  by  a  thin  platinum 
film  on  the  incident  and  on  the  emergent  side  have  been  investi- 
gated by  Robinson1  simultaneously  with  the  numbers.  In  Fig.  25 
the  curve  A  represents  the  variation  in  the  ratio  of  the  numbers 
emitted  on  the  two  sides,  and  curve  B  the  variation  in  the  ratio 
of  the  maximum  emission  energies,  with  the  thickness  of  the  film. 
The  results  as  to  the  ratio  of  the  numbers  of  the  photo-electrons 
are  open  to  criticism  on  the  grounds  of  Partzsch  and  Hallwachs' 
experiments.  But  the  criticism  does  not  apply  to  the  ratio  of  the 
velocities.  Continuing  curve  B  backwards  we  get  an  estimate  of 
the  ratio  which  would  correspond  to  a  very  thin  film  from  which 


100  200  300  sec: 

Time  of  deposit 

Fig.  25. 
Thickness  of  film  assumed  to  be  proportional  to  time  of  deposit. 

disturbing  influences  are  absent.  This  limiting  ratio  for  the 
maximum  emission  energies  comes  out  as  1*12.  The  excess  of 
energy  on  the  emergent  side  suggests  that  the  electrons  are 
originally  ejected  from  the  molecules  in  the  direction  of  the  light, 
and  that  a  loss  of  energy  occurs  when  they  swing  round  so  as  to 
emerge  on  the  incident  side.  In  the  experiments  recorded  on  pp.  40 
and  41  it  will  be  noticed  that  the  energy  of  the  photo-electrons 
deviates  from  that  predicted  by  the  quantum  theory  by  about  10  °/0 
to  25  %  according  to  the  nature  of  the  metal.  For  platinum,  the  devi- 
ation  is  14  °/o-  But  this  is  practically  identical  with  the  difference 

1  Robinson,  Phil.  Mag.  xxv.  p.  115,  1913. 


A)- 


96  PHOTO-ELECTRICITY  [CHAP. 

between  the  emission  energies  on  the  emergent  and  on  the  incident 
sides.  Hence  we  should  expect  a  good  agreement  between  the 
quantum  theory  and  experiments  if  we  considered  the  electrons 
which  emerge  with  the  light.  The  quantum  theory  does  not  of 
course  explain  the  nature  of  the  process,  it  only  deals  with  energies 
transferred.  Should  this  view  be  the  correct  one,  viz.  that  the 
quantum  theory  accounts  for  the  energies  of  the  photo-electrons 
in  a  quantitative  manner,  it  affords  still  another  example  of  the 
occurrence  of  the  constant  h  in  physics. 

The  experimental  evidence  on  this  point  is  very  meagre  and 
not  altogether  convincing,  and  much  more  is  wanted  to  test  the 
view  advanced.  Since  the  energies  of  the  photo-electrons  depend 
only  on  the  wave-length,  it  is  not  clear  why  the  ratio  (curve  B) 
decreases  with  increasing  thickness,  unless  perhaps  the  shorter 
waves  are  gradually  cut  out  by  the  increasing  thickness.  From 
optical  theory,  however,  one  would  expect  the  shorter  waves  to 
penetrate  deeper  than  the  longer  waves. 

The  Electro-magnetic  Theory  and  Asymmetry. 

The  electro-magnetic  theory  of  light  does  not  indicate  any 
asymmetry  of  a  measurable  order  in  the  photo-electric  effect. 
Richardson's  treatment1  is  as  follows.  If  E  is  the  energy  imparted 
by  light  to  an  absorbing  system,  then,  on  the  electro-magnetic 
theory,  the  momentum  imparted  is  E/c,  where  c  is  the  velocity  of 
light.  Now  consider  an  electron  absorbing  hn  units  of  energy. 
It  will  also  absorb  hn/c  units  of  momentum.  Then  the  mean 
kinetic  energy  of  the  electrons  will  be 


where   v2   is   the   mean   square"    of    me   velocities.     The   average 
momentum  in  the  onward  direction  will  be 

hn 
c  ' 
where  u  is  the  average  component  of  the  velocity  in  the  onward 

direction.     Hence 

u      v 

1  Richardson,  Phil.  Mag.  xxv.  p.  144,  1913. 

u     *Av 


,    su^r 

,"~    V 


VI ]      PHOTO-ELECTRIC   PROPERTIES  OF  THIN   METALLIC   FILMS       97 

For  electrons  whose  velocity  is  6  x  109cm./sec.,  this  yields  an 
asymmetry  of  J^,  which  is  of  the  order  of  the  asymmetry  in 
the  ionisation  on  either  side  of  a  thin  sheet  struck  by  Rontgen 
rays.  But  for  photo-electrons,  whose  velocity  is  about  6  x  107cm./sec., 
the  ratio  u/v  is  only  T^  and  therefore  we  should  not  expect  any 
measurable  asymmetry. 

Swann1  investigated  the  direct  effect  of  the  electric  and  magnetic 
forces  in  a  beam  of  light  on  a  free  electron  and  arrived  at  the  same  *  % 
result  as  Richardson  for  the  component  of  velocity  in  the  onward 
direction.  Thus  the  classical  electro-magnetic  theory  leads  to  a 
measurable  asymmetry  for  the  ionisation  by  Rontgen  rays,  but  not 
&Y  photo-electric  effects. 

C        It  is  assumed  in  the  foregoing  discussion  that  a  photo-electron 

J acquires  its  energy  from  the  light.     We  have  seen  before  that  it  is 

R  not  easy  to  reconcile  this  view  with  the  conception  of  a  continuous 

'.  \  wave  front.     To  explain  the  photo-electric  effect,  while  retaining 

the  conception  of  a  continuous  wave  front,  it  seems  necessary  to 

introduce  some  kind  of  a  resonance  system  in  which  light  produces 

instability  and  causes  the  electron  to  be  emitted  with  the  energy 

it  had  in  its  orbit.     The  investigation  of  a  resonance  system  of  this 

kind  for  asymmetric  emission  when  acted  on  by  the  forces  in  a 

light  wave  has  not  been  done  and  would  probably  be  difficult. 

^Peculiarities  in  the  Photo- Electric  Properties  of  thin  Films. 

Dike2  investigated  the  way  in  which  the  velocities  of  photo- 
electrons  (on  the  incident  side  only)  from  thin  platinum  films  varied 
with  the  thickness.  Extraordinarily  high  velocities  were  obtained, 
the  greatest  corresponding  to  about  50  volts.  Values  exceeding  15 
or  20  volts  were  very  frequently  obtained.  The  velocities  were 
highest  when  the  thickness  of  the  film  was  between  10~8  and 
10~7  cm.;  thicker  films  gave,  on  the  whole,  smaller  velocities,  though 
still  big  compared  with  velocities  usually  obtained.  Dike  and 
Brown3  confirmed  these  results,  but  do  not  now  seem  quite  con- 
vinced that  the  experiments  indicate  that  the  photo-electrons  have 

1  Swann,  Phil.  Mag.  xxv.  p.  534,  1913. 
8  Dike,  Phys.  Rev.  xxxiv.  p.  459,  1912. 
:{  Dike  and  Brown,  Phys.  Rev.  (2)  i.  p.  254,  1913. 
H.  7 


98 


PHOTO-ELECTRICITY 


[CHAP. 


really  these  high  velocities.'  No  details  as  to  the  effective  wave- 
lengths in  Dike's  experiments  are  given,  but  it  appears  that  ultra- 
violet light  was  necessary.  The  photo-electrons  from  thin  films  in 
Robinson's  experiments1  did  not  possess  exceptional  velocities. 

Emission  velocities  corresponding  to  values  as  high  as  10  volts 
are  quite  incapable  of  interpretation  on  the  quantum  theory. 
Values  less  than  the  theoretical  value  can  be  accounted  for  in 
various  ways,  but  values  in  excess  cannot  be  explained  away.  It 
seems  very  probable  that  the  abnormal  velocities  are  due  to  the 
abnormal  contact  potential  differences  between  the  illuminated 
surface  and  the  surrounding  electrode.  Very  considerable  surface 
polarisation  at  the  electrodes  exists  when  a  discharge  has  recently 


Photo  electric 
current 


Emergent  effect 


50 


Time  of  deposit 
160  1 50  sec. 

Fig.  26. 


Thickness  of  film  assumed  to  be  proportional  to  time  of  deposit. 
100  sec.  corresponds  to  10~7  cm. 

passed  through  the  apparatus  (von  Baeyer  and  Tool).  It  is  very 
probable  that  if  the  contact  potential  were  measured  at  the  same 
time  as  the  velocity  experiments  were  made,  the  high  velocities 
would  be  accounted  for. 

Robinson1  found  that  the  photo-electric  current  from  a  thin 
platinum  film  increased  very  rapidly  with  the  thickness  up  to 
10~7  cm.,  and  then  fell  off  again  (Fig.  26).  As  the  thickness  of  the 
film  increases,  more  light  is  absorbed  and  consequently  one  would 


1  Eobinson,  Phil.  Mag.  xxv.  p.  115,  1913. 


Yl]      PHOTO-ELECTRIC   PROPERTIES  OF   THIN   METALLIC   FILMS      99 

expect  the  photo-electric  effect  to  increase  with  the  thickness  though 
hardly  so  rapidly  as  it  does.  But  we  must  bear  in  mind  that  very 
thin  metallic  films  may  perhaps  absorb  less  light  than  that  calcu- 
lated by  the  ordinary  exponential  law  of  absorption  and  thus  a 
more  rapid  increase  might  be  accounted  for.  The  meaning  of  the 
term  "thickness  of  film"  becomes  rather  indefinite  when  we  deal 
with  distances  of  the  order  of  a  few  molecular  diameters.  It  was 
at  a  thickness  of  about  10~7  cm.  that  Patterson  found  that  the 
electrical  resistance  of  a  film  began  to  deviate  from  the  calculated 
values. 


7—2 


CHAPTER  VII 

PHOTO-ELECTRIC    EFFECTS    OF    NON-METALLIC    ELEMENTS 
AND    INORGANIC  COMPOUNDS 

WE  have  seen  that  the  photo-electric  effect  for  metals  sets  in 
at  a  definite  wave-length  characteristic  of  the  metal.  The  formula 
giving  the  relation  between  the  maximum  emission  energies  and 
the  frequency 

V=kn-V0 

indicates  that  there  is  no  photo-electric  effect  with  frequencies  less 
than  tt0  =  F0/A;,  or  with  wave-lengths  longer  than  X0  =  c/n0.  V0e  is 
the  work  expended  in  escaping  from  the  parent  molecule,  and  this 
is  least  for  the  electro-positive  metals.  Though  we  have  but  few 
experiments  on  the  velocities  with  which  photo-electrons  escape 
from  compounds,  yet  analogy,  and  the  experiments  we  have,  lead 
us  to  assume  that  the  same  law  holds  for  compounds  as  for  metals. 
We  can  therefore  calculate  from  the  long  wave-length  limit  the 
work  required  for  an  electron  to  escape  from  its  parent  molecule 
whatever  this  may  be. 

Sir  J.  J.  Thomson  has  introduced  the  conception  of  corpuscular 
pressure  in  molecules  (Corpuscular  Theory  of  Matter,  p.  119). 
In  metals  such  as  sodium,  the  corpuscular  pressure  is  high  and 
an  electron  is  easily  detached.  When  the  corpuscular  pressure  is 
low  as  in  chlorine,  which  has  a  great  avidity  for  electrons,  much 
more  work  is  required  to  detach  an  electron.  Photo-electrons  are 
easily  obtained  from  sodium  with  visible  light,  but  even  the  shortest 
wave-lengths  available  fail  to  ionise  chlorine.  When  two  elements 
combine,  we  may  consider  an  equalization  of  the  corpuscular  pressures 
to  take  place.  The  difference  in  the  corpuscular  pressures  is  in- 
dicated by  the  heat  of  formation  which  is  great  or  small  as  the 


CHAP.  VIl]      PHOTO-ELECTRIC   EFFECT   OF 


corpuscular  pressures  of  the  combining  elements  differ  much  or 
little.  When  an  electro-positive  substance  like  sodium  combines 
with  oxygen,  a  great  reduction  in  the  corpuscular  pressure  takes 
place,  and,  corresponding  to  this,  the  long  wave-length  limit  of  the 
photo-electric  effect  is  removed  far  into  the  ultra-violet.  On  the 
other  hand,  little  heat  is  developed  when  a  halogen  combines  with 
silver,  and  the  photo-electric  effects  in  the  metal  and  in  the  compound 
are  of  the  same  order.  Another  illustration  is  the  small  effect  in  the 
oxides  of  the  metals  compared  with  the  effect  in  the  sulphides 
which  are  sometimes  of  the  same  order  of  activity  as  the  metals 
themselves.  The  heats  of  formation  of  the  oxides  are  generally 
considerably  greater  than  those  of  the  sulphides.  Also  the  effect 
for  oxygen  starts  at  XI  350,  while  sulphur  is  sensitive  to  the  light 
from  a  mercury  lamp.  With  the  evidence  at  present  available,  one 
can  only  conclude  that  this  view  is,  in  general,  qualitatively  correct. 
The  departures  from  quantitative  agreement  are  more  marked 
when  we  compare  compounds  of  different  types.  It  is  evident 
that  in  comparing  compounds  containing  elements  of  different 
valencies,  the  valency  has,  in  some  way,  to  be  taken  into  con- 
sideration in  addition  to  the  heat  of  formation. 

When  we  collect  the  experimental  results,  we  find  that  in 
almost  all  experiments  the  only  thing  measured  is  the  total  photo- 
electric effect  and  that  the  light  is  usually  unresolved.  /  Informa- 
tion as  to  the  velocities  of  the  photo-electrons  and  as  to  the  active 
spectral  region  is  generally  wanting.  (  As  a  rule,  light  penetrates 
deeper  into  compounds  than  into  metals;  hence  if  photo-electrons 
of  the  same  number  and  velocity  are  produced  in  both  cases,  fewer 
emerge  from  the  compounds  than  from  the  metals.  I  This  is  im- 
portant, and  should  be  borne  in  mind  when  comparing  photo-electric 
effects.  As  an  approximation,  however,  (we  may  conclude  that  the 
greater  the  total  photo-electric  effect  is,  the  nearer  to  the  visible 
is  the  long  wave-length  limit  of  the  active  spectral  region./  The 
accuracy  of  this  conclusion  depends  upon  the  considerations 
mentioned  above  of  the  rapidity  with  which  the  light  is  absorbed. 

A  large  number  of  the  substances  to  be  mentioned  are  more 
or  less  insulators  and  this  has  to  be  met  by  special  experimental 
arrangements.  When  the  material  is  laid  on  a  metal  tray  in  thin 
layers,  quite  a  small  conductivity  will  suffice  to  keep  the  illuminated 


102  i  / :  V  J  { ^ :  '  :  v\  PHOTO-ELECTRICITY  [CH AP. 

surface  at  the  same  potential  as  the  tray.  But  if  the  material 
insulates,  the  surface  will  charge  up  positively  as  the  photo-electrons 
stream  away,  until  the  potential  is  high  enough  to  prevent  the 
escape  of  more.  This  gives  a  quasi-fatigue  effect,  but  the  term 
fatigue  in  this  connection  should  be  avoided  as  it  leads  to  confusion 
with  the  phenomenon  observed  in  metals.  One  way  in  which  the 
accumulated  charge  has  been  measured  is  to  transfer  the  charged 
material  into  a  Faraday  cylinder  connected  to  an  electrometer. 
The  deflection  of  the  electrometer  is  proportional  to  the  charge  on 
the  material  inside  the  Faraday  cylinder.  If  the  material  is  only 
a  fair  insulator,  then  time  will  enable  the  charge  to  dissipate  away 
so  as  to  leave  the  material  at  zero  potential.  If  however  the 
material  is  a  very  good  insulator,  this  process  takes  too  long  and 
it  is  necessary  to  start  with  fresh  material  for  each  experiment. 

Elements. 

The  gaseous  elements  whose  photo-electric  effects  have  been 
investigated  are  dealt  with  in  the  chapter  on  ionisation  in  gases. 
Only  a  few  of  the  other  non-metallic  elements  have  been  examined 
photo-  electrically. 

The  author1  found  that  arsenic  and  selenium  gave  off  photo- 
electrons  when  illuminated  by  the  light  from  a  mercury  lamp. 
The  same  law  between  the  velocity  and  the  frequency  held  for 
these  two  elements  as  for  the  metals.  The  longest  wave-length 
which  was  effective  in  exciting  the  emission  of  photo-electrons  was 
X2360  for  arsenic  and  X2200  for  selenium.  The  author  found  that 
carbon  in  the  form  of  soot  deposited  on  a  cold  plate  from  a  xylol 
flame  was  sensitive  photo-electrically  as  far  as  X2550  or  X2600. 

The  photo-electric  effect  of  sulphur  has  been  investigated  in 
great  detail  by  Goldmann  and  Kalandyk2.  Some  peculiarities  in 
the  behaviour  of  illuminated  sulphur  are  shared  by  other  insulators 
and  it  is  desirable  to  describe  the  experiments  at  some  length. 
When  light  is  absorbed  by  a  photo-electrically  active  substance 
in  a  layer  of  appreciable  thickness,  one  would  expect  photo-electrons 
to  be  released  in  the  substance  itself  as  well  as  from  the  surface. 

1  Hughes,  Phil.  Trans.  A.  ccxn.  p.  205,  1912. 

2  Goldmann  and  Kalandyk,  Ann.  d.  Phys.  xxxvi.  p.  589,  1911. 


VII] 


PHOTO-ELECTRIC   EFFECT  OF  NON-METALS 


103 


If  the  substance  is  not  naturally  a  good  conductor,  then  the  photo - 
electrons  which  do  not  emerge  should  impart  a  slight  conductivity 
during  illumination.  In  other  words,  the  substance  has  temporarily 
a  number  of  free  electrons  and  these  account  for  the  conductivity. 
That  such  is  the  case  is  supported  by  the  experiments  of  Goldmann 
and  Kalandyk  on  sulphur  and  by  other  experiments  on  insulators. 
For  investigating  the  conductivity  effect  due  to  illumination 
apart  from  the  photo-electric  effect  at  the  surface,  the  authors  used 
the  arrangement  shown  in  Fig.  27.  It  is  essentially  a  piece  of 
sulphur  between  two  electrodes.  When  illuminated  by  a  mercury 


to  potential 


The  shaded  portion  re- 
presents sulphur. 

The  light  was  incident 
vertically  downwards 
(at  right  angles  to  the 
plane  of  the  paper). 


to  electrometer 

Fig.  27. 


lamp,  the  sulphur  acquired  a  conductivity  which  was  independent 
of  the  applied  field  up  to  400  volts  per  mm.  (Higher  voltages 
were  not  tried.  It  would  be  interesting  to  see  whether  saturation 


liight 


f ' 


'M 

to  electrometer 
Fig.  28. 


could  be  obtained  with  higher  fields.)  The  order  of  the  current 
passing  through  the  illuminated  sulphur  was  2  x  10~9  amp.  with 
this  field. 

In  the  second  form  of  apparatus  used,  the  sulphur  S,  or  other 
dielectric,  is  placed  on  a  metal  plate  M,  Fig.  28.  A  gauze  G  which 
can  be  maintained  at  any  required  potential  is  arranged  parallel 


104 


PHOTO-ELECTRICITY 


[CHAP. 


to  the  surface  of  S.  When  G  is  at  a  negative  potential,  the  electro- 
meter will  acquire  a  negative  charge  due  to  (a)  the  emission  of 
photo-electrons  from  G  to  S,  (b)  the  conductivity  produced  in  the 
thin  illuminated  layer  of  sulphur.  If  the  illuminated  layer  does 
not  reach  down  to  M,  then  a  separation  of  charges  takes  place  in 
the  thin  layer  of  sulphur  until  the  external  field  in  it  is  annulled. 
This  may  be  regarded  as  a  polarisation  of  the  dielectric  which  is 
shown  by  the  electrometer  acquiring  a  negative  charge  that  after 
a  time  becomes  constant.  This  is  the  case  shown  in  curve  III, 
Fig.  29.  If  the  illuminated  layer  reaches  down  to  the  metal  plate 


100 


12345 

Time  in  min. 

Fig.  29. 

I  =1  mm.  air. 

II  —  1  mm.  air  + 1  mm.  paraffin. 
111=  1mm.  air  +  1mm.  sulphur. 
IV  =  1  mm.  paraffin. 

M,  then  the  sulphur  does  not  insulate  and  a  final  charge  is  not 
obtained.  A  steady  state  is  reached,  after  initial  polarisation 
effects,  when  a  constant  leak  occurs  and  this  is  a  measure  of  the 
photo-electric  current  from  the  gauze  to  the  sulphur,  which  as  a 
temporary  conductor  affords  passage  for  the  electricity. 

When   G  is  at  a  positive  potential,  the  electrometer  system 
acquires  a  positive  charge  due  to  (a)  the  escape  of  photo-electrons 


PHOTO-ELECTRIC   EFFECT   OF   NON-METALS 


105 


VII] 

(if  any)  from  the  surface  of  the  sulphur  to  the  gauze,  and  (b)  the 
conductivity  induced  in  the  sulphur  leading  to  a  final  polarisation 
when  the  layer  is  thick.  If  the  layer  is  so  thin  that  the  sulphur 
conducts  throughout,  then  the  steady  current  obtained  is  a  measure 
of  the  photo-electric  effect  from  the  surface. 

In  Fig.  30  we  have  curves  for  the  case  of  a  sulphur  layer  2  mm. 
thick  and  an  air  gap  of  3  mm.  Since  the  ordinates  of  curve  II  are 
greater  than  those  of  curve  I,  we  see  that  the  polarisation  effect 
4-  photo-electric  leak  from  the  sulphur  is  greater  than  the  polarisa- 
tion effect  H-  leak  from  the  gauze.  The  polarisation  effect  is  in- 
dependent of  the  direction  of  the  field.  The  surface  effect  appears 


Tf 


234567C9 

Time  in  min 
Fig.  30. 

I  =  Gauze  at  negative  potential. 
11  =  Gauze  at  positive  potential. 

to  be  quite  big  in  comparison  with  the  polarisation  effect,  but  we 
must  be  careful  about  drawing  conclusions  from  this  as  to  the 
relative  number  of  electrons  involved  in  both  processes.  The 
transport  of  an  electron  from  the  sulphur  surface  to  the  gauze 
produces  a  much  bigger  effect  than  the  transport  of  an  electron 
through  the  very  thin  layer  of  illuminated  sulphur.  (The  electron 
involved  in  the  polarisation  effect  only  moves  a  short  distance,  and 
thus  the  induced  charge  produced  in  M  by  this  movement  is 
much  less  than  the  loss  of  charge  by  M  when  an  electron  is  actually 
transferred  from  G  to  M.)  Hence  the  method  exaggerates  the 
effect  due  to  surface  photo-electric  effect  over  that  due  to  the 


106 


PHOTO-ELECTRICITY 


[CHAP, 


induced  conductivity.  Probably  the  electrons  which  are  released 
in  the  sulphur  and  so  cause  the  conductivity  do  not  emerge  from 
the  surface  when  they  get  there  as  their  velocity  has  been  reduced 
to  that  of  a  free  electron  by  repeated  collisions.  Those  which 
emerge  are  released  from  the  surface  molecules  with  the  necessary 
emission  velocities. 

The  effect  of  thickness  is  well  shown  in  Fig.  31.  When  the 
illuminated  layer  reaches  down  to  the  metallic  backing,  then  a 
steady  leak  is  obtained.  When  the  illuminated  layer  does  not 
reach  through  the  sulphur,  then  the  leak  ceases  after  a  time  and 


500 


400 


.§    300 

ki 


4? 

s3    200 


100 


III. 


I. 

II. 

III. 


246 

Fig.  31. 
Thickness  of  sulphur  =  1  mm. 


8  in  ins 


=  '5  mm. 
=  •2—  3mm. 


the  sulphur  has  reached  its  final  state  of  polarisation.     The  curves 
show  that  the  effective  depth  of  penetration  is  about  *3  mm. 

It  is  difficult  to  determine  the  ratio  of  the  number  of  electrons 
emitted  from  the  surface  to  the  number  released  in  the  illuminated 
layer.  It  is  very  probable  that  the  latter  predominates.  It  has 
already  been  indicated  that  the  experiments  give  less  weight  to 
the  latter  effect.  Again,  in  the  transverse  effect  (i.e.  the  effect 
investigated  by  the  arrangement  shown  in  Fig.  27),  no  approach 
to  saturation  was  observed  and  hence  the  number  of  electrons  set 


VIl]  PHOTO-ELECTRIC   EFFECT   OF   NON-METALS  107 

free  per  second  by  the  light  must  be  much  greater  than  is  given 
by  the  current  divided  by  the  charge  on  an  electron.  We  may 
therefore  be  justified  in  considering  that  more  electrons  are  released 
by  the  light  in  the  illuminated  layer  than  are  emitted  from  the 
sin-face.  From  analogy  with  other  substances,  mentioned  below, 
it  is  probable  that  the  surface  effect  requires  light  of  shorter 
wave-lengths  to  produce  it  than  the  conductivity  effect  requires. 
Experiments  on  this  point  would  have  been  useful.  Goldmann  and 
Kalandyk  mention  that  the  whole  effect  is  cut  off  by  a  glass  plate 
which  probably  means  that  the  effect  requires  light  of  wave-lengths 
shorter  than  \3300  to  produce  it. 

It  is  well  known  that  selenium  becomes  a  conductor  when 
illuminated  by  visible  light,  yet  its  photo-electric  effect  only  sets 
in  at  X2200.  There  seems  little  doubt  that  the  change  in  con- 
ductivity, or  part  of  it,  arises  from  electrons  which  are  set  free 
(Ries1).  It  should  be  mentioned  that  some  experimenters  believe 
that  an  allotropic  modification  of  selenium  is  formed  by  the  light 
and  that  there  is  an  equilibrium  between  this  and  the  form  which 
is  stable  in  the  dark.  The  modification  has  the  property  of  con- 
ducting electricity.  The  results  of  experiments  on  the  conductivity 
of  selenium  appear  to  be  more  complicated  than  those  on  sulphur, 
and  it  is  possible  that  the  phenomena  cannot  be  accounted  for 
adequately  by  the  setting  free  of  electrons  and  that  some  photo- 
chemical change  takes  place  in  addition.  However,  it  seems  well- 
established  that  the  escape  of  photo -electrons  from  the  surface  of 
many  non-metallic  substances  requires  light  of  shorter  wave- 
length than  is  necessary  to  produce  the  increased  conductivity. 
In  other  words,  the  long  wave-length  limit  of  the  conductivity 
effect  is  further  towards  the  red  than  that  of  the  photo-electric 
effect.  This  view  is  supported  by  Wilson's  experiments  on  silver 
iodide,  Volmer's  experiments  on  anthracene,  Pauli's  experiments 
on  the  relation  between  fluorescence  and  the  photo-electric  effect, 
and  the  experiments  of  Lenard  and  Saeland  on  phosphorescent 
substances,  and  experiments  on  selenium.  It  is  very  probable 
that  sulphur  behaves  in  a  like  manner,  though  Goldmann  and 
Kalandyk  did  not  make  any  experiments  bearing  directly  on  this 
point. 

1  Kies,  Phys.  Zeits.  xn.  p.  530,  1911. 


108  PHOTO-ELECTRICITY  [CHAP. 

In  experiments,  arranged  as  in  the  experiment  on  sulphur, 
Fig.  28,  the  change  of  conductivity  in  the  illuminated  sheet  of 
an  insulator  can  only  produce  a  polarisation  effect,  when  the 
temporarily  conducting  sheet  is  not  in  contact  with  the  metal 
electrodes.  The  electrometer  does  not,  as  in  most  photo-electric 
experiments,  acquire  a  charge  at  a  constant  rate,  but  the  rate  of 
charging  decreases  to  zero,  indicating  that  the  final  state  of 
polarisation  has  been  reached.  This  process  has  been  called  the 
actino-dielectric  effect  to  distinguish  it  from  the  photo-electric 
effect. 

In  the  formula 

V=kn~  FOJ 

representing  the  relation  between  the  potential  corresponding  to  the 
maximum  emission  velocity  and  the  frequency,  we  have  regarded 
VQe  as  the  energy  spent  by  an  electron  in  getting  away  from  the 
surface  molecules.  If  now  less  energy  is  required  to  separate  an 
electron  from  a  molecule  inside  a  solid  or  liquid  than  to  remove 
an  electron  from  a  surface  molecule  into  the  surrounding  medium, 
we  should  expect  the  increased  conductivity  to  be  produced  by 
light  of  longer  wave-length  than  is  necessary  to  produce  the 
photo-electric  effect.  On  this  view,  F0  for  a  molecule  of  sulphur 
surrounded  on  all  sides  by  other  similar  molecules  would  be  less 
than  for  the  molecules  forming  the  surface  layer.  The  experi- 
mental results  for  a  number  of  substances  are  in  agreement  with 
this  view. 

Though  several  attempts  to  obtain  ionisation  of  iodine  vapour 
when  illuminated  by  ultra-violet  light  have  been  made,  no  investi- 
gations of  the  photo-electric  effect  in  solid  iodine  appear  to  be  on 
record. 

There  is  one  very  important  problem  in  photo-electricity  on 
which  it  is  very  desirable  to  have  information.  How  does  the 
number  of  electrons  released,  when  unit  energy  of  light  is  absorbed, 
vary  with  the  frequency  of  the  light  ?  This  information  should 
be  given  by  measuring  the  saturation  currents  through  sulphur,  or 
some  other  insulator,  when  illuminated  by  light  of  different  wave- 
lengths. The  results  would  be  useful  to  compare  with  similar 
experiments  on  gases  or  vapours. 


VIl]        PHOTO-ELECTRIC   EFFECT   OF    INORGANIC   COMPOUNDS        109 

Oxides. 

There  has  been  no  systematic  examination  of  the  photo- 
electric properties  of  oxides.  The  effect  for  oxides  and  for  most 
other  compounds  is  frequently  given  in  terms  of  the  effect  for 
smile  metal,  and  as  the  state  of  this  metal  is  not  usually  specified, 
it  is  useless  to  attach  any  quantitative  importance  to  the  numbers, 
though  they  are  useful  as  indicating  the  order  of  the  effect. 

Hallwachs1  found  that  the  effect  for  CuO  and  Cu20  was  of  the 
same  order  as  that  for  Cu.  Similar  remarks  apply  to  Pb  and 
PbO2.  W.  Wilson2  found  that  PbCX  had  a  photo-electric  effect 
which  was  about  equal  to  that  of  Al  and  one  quarter  of  that  of  Ag. 
A  carbon  arc  was  used  by  both.  The  author3  found  that  CuO  gave 
a  marked  photo-electric  effect,  which  was  about  one  hundredth 
of  the  effect  for  distilled  metals  like  Pb,  Zn,  etc.  (It  should  be 
remembered  that  these  distilled  metals  give  much  bigger  effects 
than  metals  which  have  been  exposed  to  air.)  It  will  be  noticed 
that  all  the  oxides  mentioned  are  good  conductors  of  electricity. 

The  author  (I.e.)  found  that  there  was  not  a  trace  of  a  photo- 
electric emission  from  P2O5  illuminated  by  a  mercury  lamp.  BaO 
illuminated  in  the  same  way  gave  a  very  small  effect,  and  as  the 
substance  was  not  pure  it  is  possible  that  the  small  effect  was  due 
to  the  impurities.  Both  these  oxides  are  insulators.  They  possess 
bigger  heats  of  formation  than  the  other  oxides  which  show  big 
photo-electric  effects.  Hence  the  results  which  are  available  on 
oxides  support  the  view  put  forward  at  the  beginning  of  the 
chapter. 

Sulphides. 

According  to  Goldmann  and  Kalandyk's  experiments,  one  may 
conclude  that  sulphur  is  certainly  photo-electric  with  wave-lengths 
longer  than  X2000.  Hence  one  would  expect  the  photo-electric 
effect  of  a  sulphide  to  set  in  between  this  limit  and  that  of  the 
metal.  Also  if  the  combination  is  not  a  vigorous  one,  the  long- 
wave-length limit  of  the  metal  should  not  be  displaced  much. 

1  Hallwachs,  Comptes  Rendus  Congres  Radiologie,  p.  2,  1910. 
-  W.  Wilson,  Ann.  d.  Phys.  xxm.  p.  107,  1907. 
3  Hughes,  Phil.  Mag.  xxiv.  p.  308,  1912. 


110  PHOTO-ELECTRICITY  [CHAP. 

Experiments  on  this  point  have  not  been  made,  but,  if  the  total 
photo-electric  effect  of  a  sulphide  is  of  the  same  order  as  that  of 
the  metal,  we  may  conclude  that  the  long  wave-length  limits  of 
both  are  approximately  the  same.'  We  may  also  assume  that  the 
greater  the  difference  between  the  total  photo-electric  effects,  the 
greater  is  the  separation  between  the  corresponding  long  wave- 
length limits. 

The  most  systematic  experiments  on  the  sulphides  are  those 
of  B^de1.     He  found   that   the   photo-electric   current   from   a 
I  sulphide  depended  very  largely  on  its  compactness.     Chemically 
1  prepared  sulphides  were  much  less  active  than  the  minerals.     If 
however  they  were  compressed  into  a  pastille  under  a  pressure  of 
8000  atmospheres,  they  gave  much  the  same  effect  as  the  corre- 
sponding mineral  sulphides.      The   light  used  was  from  a   zinc 
spark. 

The  following  table  gives  the  photo-electric  currents  from 
various  sulphides  together  with  the  currents  from  aluminium  and 
zinc  under  similar  conditions: 

PbS  887  Fe7S8  122 

Cu2S  534  NiS  102 

CuS  391  CoAsS  89 

Zn         530                     MnS  355  ZnS  80 

Al         200                    Ag2S  240  FeS  64 

SnS  236  CdS  58 

FeS2  176  Sb2S5  45 

Cr2S3  160  CoS  29 

MnS2  141    .  MoS  28 

Bi2S3  138 

The  sensitiveness  is  of  the  same  order  as  that  of  the  metals 
and  in  some  cases  actually  greater.  However  we  must  remember 
that  the  metals  zinc  and  aluminium  were  not  in  the  most  active 
state.  Before  drawing  the  conclusion  that  the  sulphide  may  be  more 
active  than  the  metal,  the  effect  of  the  metal  distilled  in  vaeuo 
should  be  measured  and  compared  with  that  of  the  sulphide.  The 
metal  is  more  easily  affected  adversely  by  contact  with  the  atmo- 
sphere than  the  sulphide  and  this  may  account  for  the  sulphides 
appearing  to  have  a  bigger  effect.  The  author  found  that  the 
sensitiveness  of  cadmium  distilled  in  vacuo  wa^feduced  to  one  fifth 
1  Rohde,  Ann.  d.  Phys.  xix.  p.  935,  1906. 


VII]        PHOTO-ELECTRIC  EFFECT  OF   INORGANIC   COMPOUNDS        111 

by  contact  for  15  minutes  with  dry  oxygen  at  a  pressure  of  150  mm. 
Knoblauch1,  and  Ramsey  and  Spencer2  have  obtained  big  effects 
with  a  number  of  sulphides. 

Herrmann's  results3  are  in  general  agreement  with  those  of 
Rohde.  The  tellurides  and  selenides  of  the  metals,  like  the 
sulphides,  "give  big  effects^ 

>und  that  AgS  was  from  two  to  three  times 
as  active  as  silver.  In  both  cases  only  ultra-violet  rays  were 
effective.  -» 

Schmidt4  obtained  either  very  little  or  no  effect  with  CaS,  Ba^, 
and  SrS,  but  very  big  effects  with  other  sulphides  in  which  the 
metals  were  not  so  strongly  basic.  The  corresponding  sulphates 
were  not  photo-electrically  active  at  all,  hence  the  addition  of 
oxygen  to  the  molecules  shifts  the  long  wave-length  limit  beyond 
the  range  of  the  light  (spark)  used. 

Salt*. 

The  halogen  salts  of  silver  have  been  known  to  be  photo- 
electric for  some  time.  Pochettino5  gives  the  copper  halides  in 
order  of  their  photo-electric  effect  as  CuI2,  CuBr2,  CuCl2and  CuF2. 
It  is  rather  significant  that  this  is  the  order  of  increasing  stability 
and  the  order  of  decreasing  photo-electric  effect.  As  an  indication 
of  the  magnitude  of  the  effect  it  may  be  mentioned  that  the  effect 
for  CuO  is  intermediate  between  that  for  CuCl2  and  CuF2. 

Reboul6  found  that  the  photo-electric  effect  of  copper  bromide 
increased  with  continued  illumination  and  this  was  accompanied 
by  a  decomposition  of  the  salt.  After  a  prolonged  illumination 
the  effect  began  to  decrease  again,  probably  owing  to  the  fatigue 
of  the  copper. 

The  author7  found  that  much  more  satisfactory  and  consistent 
results  could  be  obtained  when  the  salts  investigated  were  distilled 
in'vacuo.  Only  under  such  conditions  could  one  be  certain  that 

1  Knoblauch,  Zeit*.  phy*.  chem.  xxix.  p.  527,  1898. 

2  Ramsey  and  Spencer,  Phil.  Mug.  xn.  p  397,  1906. 
:l  Herrruaun,  Dissertation,  Berlin,  1908. 

4  Schmidt,  Ann.  d.  Phys.  LXIV.  p.  708,  1898. 

5  Pochettino,  Arcad.  Lined,  Atti,  xv.  p.  355,  1906. 

6  Reboul,  Coinpte*  Rendus,  CLIV.  p.  424,  1912. 

7  Hughes,  Phil.  Mag.  xxiv.  p.  380,  1912. 


112  PHOTO-ELECTRICITY  [CHAP. 

the  surface  layer  was  identical  with  the  rest  of  the  substance. 
This  method  restricted  the  range  of  the  investigation  to  those  salts 
which  volatilized  at  or  below  a  red  heat.  The  apparatus  used  is  shown 
in  Fig.  11,  p.  38,  and  the  procedure  was  the  same  as  in  the  experi- 
ment on  distilled  metals.  The  light  was  obtained  from  a  mercury 
lamp.  The  following  results  for  mercurous  chloride  are  typical : 

Mercurous  chloride. 

Photo-electric  current 

f  First  20  sees.  <  '7  x  10  ~ l5  amp. 
First  exposure  after  distillation        J  Next      „  3*5  „ 

[Next      „  5-7 

Exposed  5  mins.  26*4          „ 

5  „  40-5 

In  dark  6     „  40'5          „ 

6  „  35-0 
Exposed  4  53'7          „ 

6     „  70-4 

Hence  mercurous  chloride  is  not  photo-electrically  active  in  the 
first  few  seconds  during  which  it  is  exposed  to  the  light.  The 
photo-electric  current  increases  rapidly  with  the  exposure  but  is 
checked  by  shutting  off  the  light.  At  the  end  of  the  experiment, 
it  was  found  that  the  distilled  salt,  originally  white,  had  a  grey 
metallic  lustre  on  the  exposed  part.  There  is  no  doubt  that  the 
explanation  is  that  the  light,  first  of  all,  decomposes  the  salt,  and 
then  produces  a  photo-electric  effect  in  the  metallic  mercury. 
Thus  the  effect  of  the  light  in  this  case  is  primarily  photo- 
chemical. A  similar  effect  was  obtained  with  HgCl2,  Hgl,  HgI2 
and  BiCl3  and  a  very  much  smaller  one  with  PbI2.  In  the  case 
of  the  iodides  of  mercury,  the  initial  leak  was  not  zero,  but  quite 
small.  Probably  the  decomposition  started  too  rapidly  to  enable 
the  initial  zero  effect  to  be  detected.  There  was  not  a  trace  of 
a  photo-electric  emission  from  ZnCl2  even  after  prolonged  exposure. 
Under  similar  conditions,  there  was  only  the  slightest  indication 
of  a  photo-electric  effect  in  FeCl3.  No  discoloration  was  produced 
in  these  salts  by  prolonged  illumination.  The  decomposition,  and 
subsequent  photo-electric  effect,  which  is  very  feeble,  or  even  non- 
existent, in  ZnCl2,  FeCl3,  and  PbI2  is  well  marked  in  the  mercury 
chlorides  and  iodides  and  in  bismuth  chloride.  The  first  three 
are  much  more  stable  salts  than  the  others. 


VI I]        PHOTO-ELECTRIC  EFFECT  OF   INORGANIC  COMPOUNDS        113 

Schmidt  (I.e.)  found  that  the  stable  salts  NaCl,  NaBr,  Nal 
and  NaF  were  not  photo-electric  with  the  light  from  a  spark, 
while  big  effects  were  obtained  with  AgCl,  AgBr  and  Agl.  The 
effects  for  the  latter  were  practically  identical.  A  large  number  of 
sulphates  and  other  salts,  usually  regarded  as  the  more  stable 
salts,  gave  no  photo-electric  effect. 

The  photo-electric  experiments  on  silver  iodide  are  of  special 
interest  as  the  silver  halides  are  peculiar  in  their  behaviour 
towards  light. 

Scholl1  found  that  silver  iodide,  a  poor  conductor  in  the  dark, 
became  a  much  better  conductor  when  illuminated.  The  wave- 
length most  effective  in  producing  the  change  in  conductivity  was 
X4330. 

W.  Wilson8  studied  the  photo-electric  effect  and  the  increase 
in  conductivity  due  to  illumination  in  silver  iodide  simultaneously. 
With  an  arc  lamp,  the  silver  iodide  was  found  to  be  ten  times  as 
active  photo-electrically  as  an  aluminium  plate.  The  silver  iodide 
was  prepared  by  depositing  a  film  of  silver  on  a  suitable  plate 
and  then  converting  it  into  the  iodide  by  iodine  vapour.  The 
change  in  conductivity  was  produced  both  by  violet  and  ultra- 
violet light,  the  effect  due  to  the  latter  being  only  8  to  10  %  of 
that  due  to  the  former.  The  emission  of  photo-electrons  only  \ 
occurred  when  ultra-violet  light  was  used.  The  absence  of  photo- 
electric effect  in  the  violet  might  be  attributed  to  the  violet  light 
penetrating  to  greater  depths  than  the  ultra-violet  light,  but  this 
view  cannot  be  correct  according  to  the  following  observations. 
Wilson  found  the  absorption  coefficient  of  silver  iodide  (referred 
to  1  mm.)  for  the  photo-electrically  active  rays  to  be  15,000. 
Scholl  found  the  absorption  coefficient  of  the  rays  most  active  in 
producing  the  increase  in  conductivity  to  be  13,000.  Hence  the 
explanation  based  on  different  penetrations  is  inadequate.  [The 
coefficient  denoted  in  optical  works  by  nk  is  '44  for  silver  iodide. 
Drude  gives  37  as  the  value  corresponding  to  green  light  for 
silver.]  It  is  somewhat  surprising  that  the  ultra-violet  light] 
produces  a  smaller  conductivity  change  than  the  violet  light./ 
Wilson  suggests  the  following  explanation:  Violet  light  causes' 

1  Scholl,  Ann.  d.  Phys.  xvi.  pp.  193,  417,  1905. 

2  W,  Wilson,  Ann.  d.  Phys.  xxra.  p.  107,  1907. 

H.  8 


114  PHOTO-ELECTRICITY  [CHAP. 

the  molecules  to  emit  electrons  with  small  velocities.  These 
are  easily  directed  by  the  applied  electromotive  force  and  so 
increase  the  conductivity.  Ultra-violet  light  releases  electrons 
of  higher  speed,  which  are  less  easily  directed  by  the  electro- 
motive force,  and  hence  the  change  in  conductivity  is  less.  In 
other  words,  the  slow  photo-electrons  are  more  easily  converted 
into  free  electrons,  which  determine  the  conductivity,  than  the 
faster  photo-electrons. 

Attempts  to  detect  a  change  of  conductivity  in  thin  metallic 
films  when  exposed  to  light  have  yielded  negative  results  because 
the  free  electrons  are  much  more  numerous  than  the  photo-electrons 
produced  (Badeker1).  This  refers  to  continuous  films.  Wilson 
produced  a  film  of  granulated  silver  which  was  practically  in- 
sulating. The  tiny  granules  are  probably  separated  by  insulating 
air  spaces  and,  in  fact,  the  preparation  is  analogous  to  a  fine-grain 
coherer.  On  illuminating  the  film  by  ultra-violet  light,  there  was 
an  increase  of  conductivity,  which  was  independent  of  the  potential 
applied.  The  conductivity  in  this  case  is  produced  only  by  light 
of  the  same  wave-lengths  as  that  which  produces  the  photo-electric 
effect  and  not  by  light  of  longer  wave-lengths  in  addition.  Photo- 
electrons  are  probably  emitted  in  all  directions  by  the  granules 
and  the  applied  potential  gives  them  a  velocity  component  and 
hence  the  conductivity.  When  silver  iodide  was  produced  in  a 
granulated  layer  like  the  granulated  silver  and  not  in  a  continuous 
layer  as  before,  the  conductivity  effect  again  went  together 
with  the  photo-electric  effect.  In  the  granulated  materials,  we 
are  concerned  with  an  emission  of  photo-electrons  from  a  large 
number  of  surfaces  within  the  substance,  and  hence  it  is  only  the 
light  which  produces  a  photo-electric  effect  that  causes  an  increase 
in  the  conductivity. 

Liquids. 

Brillouin2  found  that  water  was  not  photo-electric,  while  ice 
was.  The  author3  found  that  when  water  was  illuminated  by  the 

1  Badeker,  Leipzig.  Ber.  LV.  p.  198,  1903. 

2  Brillouin,  given  in  Sir  J.  J.  Thomson,  Cond.  Elec.  through  Gases,  p.  289. 

3  Hughes,  Phil.  Mag.  xxiv.  p.  380,  1912. 


VII] 


PHOTO-ELECTRIC   EFFECT  OF  LIQUIDS 


115 


light  from  a  mercury  lamp,  there  was  hardly  any  photo-electric 
effect  at  all. 

Obolensky1  has  made  some  useful  investigations  on  the  photo- 
electric effect  of  ice,  water  and  solutions.  He  used  the  light  from 
a  very  powerful  aluminium  spark  which  was  very  rich  in  short 
wave-lengths.  The  light  from  this  source  was  passed  through 
several  filters,  given  in  the  table.  The  quartz  plate  was  '25  mm. 
thick  and  the  calcite  plate  3  mm.  thick.  In  the  second  column 
the  limit  of  transparency  for  the  different  substances  (excepting 
calcite)  is  given  from  a  consideration  of  Lyman's  work  (Chap.  x). 
It  is  certain  that  the  limit  assigned  to  quartz  by  Obolensky,  viz. 
XI 850,  is  quite  incorrect. 


Light  filter 

Approximate 
short  wave- 
length limit 

Photo-electric  effect 

CuO 

Ice 

Water 

I.      Fluorite 
II.     Quartz 
III.    Quartz  +  air 
IV.    Calcite 
V.     Glass 

X1250 
X1450 
X1770 
X2000 
X3300 

100 
27 
22 
<1 
0 

100 
40 
50 
•02 
0 

100 
15 
11 

0 
0 

We  see  that  the  Schumann  region  is  most  active  in  producing 
a  photo-electric  effect  in  water.  Even  thin  quartz  transmits  only 
J  of  the  active  light,  while  calcite  transmits  none  at  all.  The  ' 
figures  for  cupric  oxide,  ice  and  water  are  not  comparable  with 
one  another.  The  effects  produced  by  the  light  passing  through 
fluorite  were  100,  70,  and  "25  in  cupric  oxide,  ice  and  water  re- 
spectively. Hence  ice  has  a  much  bigger  photo-electric  effect  than } 
water,  which  confirms  Brillouin's  results.  From  an  examination  of 
the  table  it  appears  that  the  photo-electric  effect  in  ice  does  not  fall 
off  so  rapidly  with  increasing  wave-length  as  the  effect  in  water. 
Before  building  on  these  experiments,  we  should  know  what  the 
penetrating  power  of  light  of  short  wave-length  is  in  water  and  in 
For  if  the  light  were  absorbed  in  a  thin  layer  in  ice  and  in 


ice. 


1  Obolensky,  Ann.  d.  Phys.  xxxix.  p.  961,  1912. 


8—2 


116 


PHOTO-ELECTRICITY 


[CHAP. 


a  thicker  layer  in  water,  then  relatively  fewer  photo-electrons 
would  emerge  from  the  water.  There  is  no  available  information 
on  this  point.  But,  if  we  may  disregard  the  "02  in  the  column 
for  ice,  the  long  wave-length  limit  is  much  the  same  for  ice  as 
for  water. 

From  these  results,  it  appears  that  there  is  a  photo-electric 
effect  in  water  with  wave-lengths  longer  than  XI 7  70,  but  there  is  no 
effect  with  X2000.  From  the  results  of  the  author,  we  can  perhaps 
get  closer  limits.  Since  the  shortest  wave-length  in  the  mercury 
lamp  cannot  be  said  to  produce  any  definite  photo-electric  effect, 
the  photo-electric  effect  for  water  must  set  in  between  XI 7  70  and 
X1850.  Oxygen  is  ionised  only  by  wave-lengths  less  than  X1350, 
while  hydrogen  has  not  been  ionised  at  all.  It  is  rather  surprising 
therefore  that  water  should  be  photo-electric  with  longer  waves. 
Strictly  speaking  however,  the  effect  should  be  compared  for  the 
gaseous  state  in  all  cases,  or  for  the  liquid  state. 

Traces  of  impurities  do  not  produce  any  appreciable  effect  on 
the  photo-electric  properties  of  water. 

With  salt  solutions,  the  following  results  were  obtained.  The 
light  used  was  that  transmitted  through  fluorite. 


Concentration 

NaCl 

KC1 

Na2S04 

K2SO4 

NaN03 

Na2CO;i 

0 

100 

100 

100 

100 

100 

100 

2% 

85 

35 

325 

156 

10% 

50 

30 

465 

360 

411 

397 

15% 

50 

30 

560 

540 

The  electro-negative  ion  in  the  salt  appears  to  determine 
whether  the  effect  increases  or  decreases.  The  chlorides  all 
decrease  the  effect  and  it  is  well  to  note  that  the  chlorine  is  the 
most  electro-negative  of  the  acid  ions.  Though  the  acid  ions 
appear  to  determine  the  behaviour  of  the  solution  very  largely, 
20  °/0  of  sulphuric  acid  did  not  alter  the  effect  of  pure  water. 
Experiments  showed  that  the  active  spectral  region  is  displaced 
somewhat  to  the  ultra-violet  for  the  chlorides  and  to  the  longer 
wave-lengths  for  the  other  salts. 

In    connection    with    these    experiments    on    solutions,  it  is 


Vll]  PHOTO-ELECTRIC   EFFECT  OF   INSULATORS  117 

convenient  to  refer  to  two  experiments  by  the  author1.  It  was 
found  that  zinc  chloride  and  phosphorus  pentoxide,  sublimed  in 
vacuo,  had  not  the  slightest  trace  of  a  photo-electric  effect  when 
the  light  from  a  mercury  lamp  was  used.  On  admitting  ordinary  air 
for  a  time  and  then  pumping  it  out,  the  surface  of  both  substances 
bf  came  more  or  less  wet.  In  this  state,  they  had  a  big  photo- 
electric effect,  far  larger  than  could  be  accounted  for  by  the  water 
effect  (if  any)  with  the  wave-lengths  available.  It  is  difficult  to 
see  why  a  concentrated  solution  of  zinc  chloride  or  phosphorus 
pentoxide  should  be  very  much  more  photo-electric  than  either 
solute  or  solvent. 

Before  leaving  this  part  of  the  subject,  some  remarks  should 
be  made  on  certain  photo-electric  experiments  in  which  liquids 
are  involved.  Jaffe2  found  that  an  illuminated  zinc  plate  immersed 
in  hexane  gave  off  negative  electricity,  the  amount  being  of  the 
order  of  one  thousandth  of  that  for  zinc  immersed  in  air  in  the 
ordinary  way.  Almost  all  the  effect  was  due  to  the  zinc,  and  no 
part  of  it  could  be  definitely  attributed  to  a  volume  effect  in  hexane. 

More  recently,  Volmer3  has  shown  that  hexane  is  not  ionised 
by  the  light  from  a  mercury  lamp.  The  experiments  of  Szivessy 
and  Schafer4  on  the  ionisation  of  paraffin  oil  by  ultra-violet  light 
from  a  mercury  lamp  are  inconclusive,  and  there  was  nothing  to 
show  that  the  effect  found  was  not  due  (as  in  Jaffe's  experiments) 
to  photo-electric  action  of  the  light  at  the  metallic  electrodes. 

Insulators. 

The  results  of  a  few  miscellaneous  experiments  which  can 
hardly  be  classified  elsewhere  are  given  here. 

Reiger3  investigated  the  photo-electric  effect  of  a  number  of 
insulators,  using  an  arc  lamp  as  the  source  of  light.  Due  care 
was  taken  to  avoid  spurious  results  arising  from  the  charging 
up  of  the  surface  of  these  insulators.  The  photo-electric  effect 
was  small  for  the  insulators  tried,  being  much  less  than  that  for 
carbon. 

1  Hughes,  Phil.  Mag.  xxiv.  p.  380,  1912. 

2  Jaffe,  Phys.  Zeits.  xi.  p.  571,  1910. 

3  Volmer,  Ann.  d.  Phys.  XL.  p.  775,  1913. 

4  Szivessy  and  Schafer,  Ann.  d.  Phys.  xxxv.  p.  511,  1911. 

5  Reiger,  Ann.  d.  Phys.  xvn.  p.  935,  1905. 


118  PHOTO-ELECTRICITY  [CHAP.  VII 

The  following  are  relative  values  : 

Ebonite           specimen  1  17 '8 

„  2               70-0 

„  3  33-8 

Mica  18-8 

Sealing-wax  35 '2 

Beeswax  2'3 

Resin  16 '4 

W.  Wilson  (I.e.)  found  that  shellac  had  a  photo-electric  effect 
about  JQ  that  of  aluminium.  Goldmann  and  Kalandyk  (i.e.) 
also  found  that  shellac  was  photo-electric.  They  found  in  addition 
that  its  conductivity  increased  when  illuminated,  showing,  as  in 
the  case  of  sulphur,  that  photo- electrons  were  released  in  the 
substance.  No  permanent  polarisation  as  a  result  of  illumination 
could  be  obtained.  Owing  to  its  slight  conductivity,  shellac 
would  not  charge  up  permanently  like  sulphur.  No  appreciable 
photo-electric  effect  was  shown  by  paraffin  or  by  paraffin  oil  when 
illuminated  by  a  mercury  lamp. 


CHAPTER  VIII 

PHOTO-ELECTRIC    EFFECTS    OF    DYES,    FLUORESCENT    AND 
PHOSPHORESCENT    SUBSTANCES 

HALLWACHS1  and  Stoletow2  were  the  first  to  show  that  a 
number  of  organic  dyes  were  photo-electric  when  illuminated  by 
light  of  short  wave-length.  Schmidt3  concluded  that  there  was 
no  close  connection  between  fluorescence  and  photo-electric  effects. 
Fuchsine  was  found  to  be  photo-electric  when  dissolved  in  water, 
but  not  when  dissolved  in  alcohol,  while  both  solutions  are  fluor- 
escent. The  explanation  has  been  given  by  Rohde's  experiments4. 
The  reflecting  power  of  a  surface  of  a  fresh  aqueous  solution  of 
fuchsine  or  methyl  violet  increases  with  its  age.  In  fact,  a  film 
of  solid  dye  separates  out,  as  can  be  shown  by  drawing  a  glass 
rod  through  the  surface,  on  which  a  jagged  tear  is  left.  Rohde's 
method  of  recording  the  growth  of  the  film  was  to  suspend  a  sheet 
of  metal  in  the  solution  of  fuchsine  or  methyl  violet  by  a  fine 
wire.  Torsion  was  gradually  applied  until  the  surface  film  was 
torn.  The  angle  of  torsion  was  a  measure  of  the  strength  and 
thickness  of  the  film.  In  Fig.  32,  the  ordinates  represent  the  couple 
required  bo  break  films  of  methyl  violet  whose  ages  are  given 
horizontally.  The  different  curves  refer  to  solutions  of  different 
concentrations.  Now,  the  photo-electric  effect  of  the  solution  also 
increased  with  the  age,  as  is  shown  in  Fig.  33.  The  similarity  of 
the  curves  shows  without  any  doubt  that  the  photo-electric  effect 
observed  is  that  of  the  thin  solid  film  of  methyl  violet  which 

1  Hallwachs,  Wied.  Ann.  xxxvn.  p.  666,  1889. 

2  Stoletow,  Physikalische  Revue,  Bd.  i.  1892. 

3  Schmidt,  Ann.  d.  Phys.  LXIV.  p.  708,  1898. 

4  Bohde,  Ann.  d.  Phys.  xix.  p.  935,  1906. 


120 


PHOTO-ELECTRICITY 


[CHAP. 


separates  out.  There  was  no  photo-electric  effect  with  the 
alcoholic  solution,  neither  was  there  any  formation  of  a  solid 
surface  layer.  Rohde  found  that  solid  fuchsine  had  much  the 


1  — 

i  

^*~ 

,  — 

85  r     /   / 

^ 

"sn 

-2  °   /  /  > 

|J// 

•"Tv""" 

/ 

^ 

w 

/ 

8        10        12       14  hours 
Fig.  32. 
Formation  of  methyl  violet  film  on  water.     Torsion  experiments. 

I.  750  c.c.  concentrated  solution  in  f  litre  water. 

II.  375  c.c.  ,,  ,,  ,, 
in.      85  c.c. 

IV.       17  c.c. 


40 


80 


100  mms 


60 
Fig.  33. 

Formation  of  methyl  violet  film  on  water.     Photo-electric  experiments. 

I.  750  c.c.  concentrated  solution  in  |  litre  water. 

II.  375  cc. 

III.  85  c.c.  „  ,,  „ 

IV.  17  c.c. 

same  photo-electric  effect  as  the  layer  on  an  old  aqueous  solution. 
The  photo-electric  effect  of  solid  dyes  depended  to  a  considerable 


VIII]        FLUORESCENT   AND  PHOSPHORESCENT  SUBSTANCES  121 

extent  on  the  degree  of  compactness  of  the  dyes  (see  also  Rohde's 
experiments  on  sulphides). 

Stark  and  Steubing1  investigated  the  photo-electric  effect  and 
fluorescence  of  a  large  number  of  organic  substances.  The  photo- 
electric effect  of  some  of  the  substances  changed  rapidly  with 
exposure  to  the  light  (mercury  lamp)  owing  to  chemical  changes 
produced  by  the  light.  In  such  cases,  only  the  initial  effect  was 
taken  as  the  real  effect  of  that  particular  substance.  The  in- 
tensity of  the  fluorescence  was  given  in  five  grades,  arbitrarily 
estimated.  A  long  table  is  given  in  the  original  paper  containing 
the  intensity  of  fluorescence  and  the  magnitude  of  the  photo- 
electric effect  of  the  substances  investigated.  The  authors  con-, 
elude  that,  in  general,  the  more  intense  the  fluorescence,  the/ 
greater  the  photo-electric  effect,  and  consequently  that  the! 
photo-electric  effect  and  fluorescence  in  the  organic  substances  ' 
investigated  are  fundamentally  connected.  An  examination  of 
their  table  does  not  carry  conviction  as  to  the  justification  for 
their  conclusion.  When  we  remember  that  very  many  substances 
show  photo-electric  effects  with  the  source  of  light  used,  and  that 
the  photo-electric  effect  varies  enormously  with  the  state  of  the 
surface  of  any  substance  and  depends  upon  the  depth  to  which 
the  light  penetrates  and  other  conditions,  it  is  very  doubtful,  even 
if  fluorescence  and  the  photo-electric  effect  were  fundamentally 
connected,  whether  a  close  connection  would  be  shown  "in  experi- 
ments of  this  kind.  These  considerations  make  it  desirable  to 
look  for  a  relation  between  fluorescence  and  the  photo-electric 
effect  in  a  somewhat  different  way. 

Pauli2  adopted  a  method  which  possesses  some  novel  features 
for  investigating  the  problem.  The  ratio  of  the  intensity  of  the 
fluorescent  light  to  that  of  the  exciting  light  was  studied  as  a 
function  of  its  relation  to  the  wave-length  of  the  exciting  light. 
At  the  same  time,  the  photo-electric  effect  was  investigated. 
Now  if  there  is  a  fundamental  relation  between  the  two  effects, 
we  should  expect  a  marked  photo-electric  effect  with  the  most 
active  exciting  light.  Organic  fluorescent  solids  were  laid  on  a 


1  Stark  and  Steubing,  Phys.  Zeits.  ix.  p.  481,  1908. 

2  Pauli,  Ann.  d.  Phys.  XL.  p.  677,  1913. 


122 


PHOTO-ELECTRICITY 


[CHAP. 


shallow  tray  which  was  connected  to  the  electrometer.  Around 
this  tray  was  a  cylindrical  electrode,  which  could  be  raised  to  any 
desired  potential.  On  illuminating  these  fluorescent  substances 
they  all  showed  very  marked  actino-dielectric  effects  (see  p.  108). 
A  typical  case  is  given  in  Fig.  34  for  eosine.  The  two  curves  give 
the  progress  of  the  leak  with  the  time,  the  cylinder  being  at  a 
positive  or  negative  potential  relative  to  the  illuminated  substance. 
After  a  time  the  actino-dielectric  effect  disappears,  leaving  the 
photo-electric  effect,  provided  the  field  is  favourable  to  the  escape 
of  negative  electricity.  The  actino-dielectric  effect  is  independent 


\ 


\A 


Eosine 


10 
min 


Fig.  34. 


A. 
B. 


Surrounding  cylinder  at  +  potential. 
,,  ,,          ,,    -  potential. 


of  the  direction  of  the  field.  Taking  a  zinc  plate  as  a  standard  of 
reference  and  calling  its  photo-electric  effect  2000,  the  most  active 
fluorescent  substance  was  anthracene  with  10,  and  the  least  active 
eosine  with  1*2.  On  plotting  the  intensity  of  the  actino-dielectric 


A  6000  A  5000  A  4000 

Fig.  35. 

I.  Actino-dielectric  effect. 

II.  Efficiency  of  light  for  exciting  fluorescence. 


VIII]         FLUORESCENT   AND   PHOSPHORESCENT   SUBSTANCES          123 

effect  and  the  efficiency  of  the  exciting  light  against  the  wave- 
length, no  relation  at  all  was  shown  between  the  light  exciting 
fluorescence  and  that  producing  the  actino-dielectric  effect.  For 
anthracene,  the  maximum  for  the  former  was  at  X4450,  for  the 
latter  at  \5400  (Fig.  35).  In  Fig.  36  we  have  sets  of  three  curves. 
Curve  I  gives  the  distribution  of  the  fluorescent  light,  curve  II 
the  efficiency  of  the  exciting  light,  and  curve  III  the  magnitude 
of  the  photo-electric  effect.  In  no  case  did  visible  light  produce 
a  photo-electric  effect,  while  in  all  the  substances  chosen  the  light 
most  efficient  in  stimulating  fluorescence  was  in  the  green  or  blue. 
Moreover,  the  photo-electric  effect  always  increases  with  decreasing 


2, 5  —dimethoxybenzalindandion 


m — ammo- eye 


nstilben 


I 

:    : 


2, 5—dimethoxycyanstilben 


anthracene 


III 


A  6000 


A  5000 

Fig.  36. 


A  4000 


A  3000 


wave-length,  while  the  shape  of  curve  II  for  the  exciting  light 
is  characteristic  of  the  particular  substance  investigated.  Hence 
there  appears  to  be  no  connection  between  the  fluorescence  of  a 
substance  and  its  photo-electric  effect. 

Byk  and  Borck1  and  Pochettino2  have  observed  a  photo- 
electric effect  in  anthracene.  The  former  devised  a  new  method 
to  overcome  the  difficulty  met  with  in  their  experiments  by  the 
high  insulating  power  of  anthracene.  Pochettino  applied  the 
term  "  fatigue "  to  the  falling  off  of  the  photo-electric  effect  of 

1  Byk  and  Borck,  Verh.  d.  Deutsch.  Phys.  Ges.  xn.  p.  621,  1910. 

2  Pochettino,  Accad.  Lincei,  Atti,  xv.  p.  355,  1906. 


124  PHOTO-ELECTEICITY  [CHAP. 

anthracene  during  exposure  to  light.  It  is  better  to  avoid  the 
use  of  the  term  in  this  connection,  as  fatigue  in  anthracene  is 
quite  a  different  thing  from  fatigue  in  metals.  The  so-called 
fatigue  in  anthracene  is  merely  due  to  its  insulating  properties, 
which  cause  it  to  charge  up  until  its  potential  becomes  almost 
equal  to  that  of  the  opposing  electrode,  and  then  the  photo-electric 
current  ceases. 

The  author1  found  that  a  layer  of  anthracene,  distilled  in 
vacuo,  gave  off  electrons  when  illuminated  by  the  light  from  a 
mercury  lamp.  The  velocities  of  the  photo-electrons  were  in 
agreement  with  the  law  which  has  been  established  for  metals, 


The  critical  wave-length  at  which  the  effect  sets  in  for  anthracene 
is  between  \2150  and  X2200.  That  k  is  of  the  same  order  for 
anthracene  as  for  the  metals  points  to  the  identity  of  the  photo- 
electric process,  whether  in  metals  or  in  organic  bodies  of  very 
different  chemical  constitution.  In  fact  (excepting  Pohl  and 
Pringsheim's  selective  effect  for  the  alkali  metals)  the  only 
characteristic  in  the  photo-electric  effect  which  depends  on  the 
substance  used  is  the  long  wave-length  limit. 

Stark  looked  for  an  increased  conductivity  in  a  fluorescing 
solution  of  anthracene  in  benzol  and  in  hexane,  but  with  negative 
results.  Volmer2  has  obtained  some  useful  results  from  experi- 
ments on  anthracene  dissolved  in  hexane.  He  also  confirmed  the 
result  given  above,  that  anthracene  in  vacuo  does  not  give  off 
photo-electrons  unless  it  is  illuminated  by  wave-lengths  shorter 
than  X2250.  Before  commencing  the  experiments  on  solutions  of 
anthracene  the  hexane  was  repeatedly  purified  until  its  conduc- 
tivity in  the  dark  and  due  to  illumination  became  negligible. 
Then  any  small  effect  due  to  the  conductivity  of  the  illuminated 
solution  of  anthracene  could  be  detected  and  attributed  to  the 
dissolved  anthracene.  An  arc  lamp  was  used  in  these  experiments. 
In  Volmer  's  experiments  on  the  conductivity  of  illuminated  an- 
thracene solutions  there  appear  to  be  two  distinct  effects.  One 


1  Hughes,  Phil.  Mag.  xxiv.  p.  380,  1912. 

2  Volmer,  Ann.  d.  Phys.  XL.  p.  775,  1913. 


VIII]         FLUORESCENT   AND   PHOSPHORESCENT   SUBSTANCES  125 

is  a  direct  photo-electric  effect  and  the  other  is  a  conductivity 
apparently  arising  out  of  a  photo-chemical  process  in  which  the 
anthracene  splits  up  into  positive  and  negative  ions.  With  wave- 
lengths longer  than  X2250  there  is  no  trace  of  a  conductivity  due 
to  a  volume  ionisation  of  the  fluorescing  anthracene  solution.  But 
when  the  solution  is  saturated,  and  only  then,  a  conductivity  due 
to  illumination  appears,  which  was  traced  to  an  effect  localized 
at  the  thin  layers  of  precipitated  anthracene  at  the  electrodes. 
Volmer  suggests  that  some  anthracene  molecules  are  split  up  by 
the  light  into  positive  and  negative  ions  which  go  into  solution 
and  follow  the  electric  field.  [Note. — A  similar  experiment  was 
tried  with  sulphur,  which  is  only  slightly  soluble  in  hexane. 
Evidence  was  obtained  that,  in  this  case,  only  the  positive  ions 
went  into  solution.]  Light  of  wave-length  longer  than  \2250  was 
also  found  to  increase  the  conductivity  of  solid  anthracene,  but  did 
not  produce  a  photo-electric  effect.  It  may  repay  investigation  to 
examine  whether  there  is  any  further  connection  between  the  con- 
ductivity produced  in  solid  anthracene  by  wave-lengths  longer 
than  X2250  and  this  new  effect  in  illuminated  solutions. 

When,  however,  wave-lengths  shorter  than  \2250  are  used,  the 
solution  is  found  to  acquire  a  conductivity  due  to  volume  ionisation. 
Probably  photo-electrons  are  emitted  from  the  anthracene  mole- 
cules and  become  negative  ions  leaving  a  positive  anthracene 
molecule.  (This  view  could  be  tested  by  mobility  experiments, 
for  the  negative  ion  would  be  a  molecule  or  cluster  of  molecules  of 
the  solvent  only,  while  the  positive  ion  necessarily  contains  an 
anthracene  molecule.)  With  these  short  wave-lengths  the  slightest 
trace  of  anthracene  in  the  hexane  produces  a  very  marked  increase 
in  the  conductivity  on  illumination,  the  order  being  100 — 300 
times.  The  conductivity  is  directly  proportional  to  the  amount  of 
liquid  illuminated.  As  the  potential  difference  increases,  the 
current  becomes  almost  saturated  between  320  and  640  volts. 
The  maximum  conductivity  occurs,  in  the  particular  form  of  cell 
used,  when  the  concentration  of  the  anthracene  is  '00025  normal. 
Greater  concentrations  caused  the  light  to  be  completely  absorbed 
in  too  thin  a  layer  close  to  the  window. 

Other  substances  dissolved  in  hexane  were  tested  and  the 
volume  ionisation  measured.  The  results  are  given  in  the 


126 


PHOTO-ELECTRICITY 


[CHAP. 


following  table,  together  with  Stark's  relative  values  for  the  photo- 
electric effect  of  the  solid  substances. 


Substance 

Conductivity  of 
solution 

Kelative  photo-electric 
effect  for  solute 

Naphthalene 
Phenol 

0 
0 

1-2 
2-2 

Phenanthrene 

6 

8-2 

Diphenylmethane 
/3-Phenol 

7 
10 

17-0 
10-6 

Anthracene 

20 

12-5 

a-Naphthylamine 
Diphenylamine 

40 
50 

15-0       ^ 
17-0 

It  is  clear  that  the  increased  volume  conductivity  of  a  solution 
is  very  closely  connected  with  the  photo-electric  effect  of  the  cor- 
responding solute.  This  was  also  checked  by  using  absorption 
screens  for  the  light.  The  two  effects  for  anthracene,  solid  and  in 
.  solution,  went  together.  The  anthracene  molecule,  when  suitably 
*  illuminated,  loses  an  electron,  this  electron  sticks  to  the  nearest 
neutral  molecule,  and  thus  we  get  the  necessary  conditions  for  the 
conductivity. 

The  region  producing  fluorescence  in  anthracene,  X4000 — A,2250, 
does  not  produce  photo-electric  effects.  The  results  of  Volmer's 
experiments,  in  addition  to  those  of  Pauli,  Schmidt,  and  Rohde  on 
fluorescent  organic  bodies,  and  those  of  Henry,  Whiddington  and 
Franck  and  Westphal  on  fluorescing  iodine  vapour,  give  us  strong 
grounds  for  concluding  that  the  electron  disturbance  associated 
with  fluorescence  has  nothing  to  do  with  the  photo-electric  effect 
It  seems  very  unlikely  that  anthracene  vapour  is  ionised  by  light 
of  wave-lengths  greater  than  X2200  (the  limit  for  solid  anthra- 
cene), but  quite  a  long  range,  extending  to  the  visible,  produces 
a  fluorescence. 

Stark1  has  shown  that,  in  a  number  of  cases,  the  benzene 
derivatives  possess  two  absorption  bands  with  which  fluorescence 
bands  are  associated.  In  most  cases,  the  long  wave-length  band 
only  has  been  shown  to  exist,  but  analogy  suggests  that  other 
fluorescent  benzene  derivatives  also  possess  a  short  wave-length 
absorption  band  far  in  the  ultra-violet.  The  fluorescence  usually 
1  Stark,  Phys.  Zeits.  ix.  p.  481,  1908 ;  Ann.  d.  Phys.  XLI.  p.  728,  1913. 


VIII]        FLUORESCENT  AND   PHOSPHORESCENT  SUBSTANCES  127 

observed  is  excited  when  light  belonging  to  the  long  wave-length 
absorption  band  is  absorbed  and  is,  as  we  have  seen,  unaccompanied 
by  photo-electric  effects.  When  light  belonging  to  the  short  wave- 
length absorption  band  falls  on  the  substance,  it  appears,  from  the 
evidence  available,  that  a  photo-electric  effect  is  produced  as  well 
as  fluorescence. 

Fluorescence  does  not  seem  to  involve  the  separation  of  an 
electron  from  its  parent  molecule,  for  in  the  cases  given  above  the 
fluorescence  is  often  most  marked  when  there  is  no  trace  of  any 
photo-electric  effect  or  any  conductivity  indicating  the  separation 
of  elections.  It  appears  as  if  the  disturbing  light  causes  the 
electron  to  be  displaced  within  the  sphere  of  influence  of  the  mole- 
cule, and  that  the  fluorescent  light  is  due  to  the  electron  settling 
clown  to  its  equilibrium  position.  The  experiments  of  Franck  and 
Westphal  indicate  that  it  is  easier  to  separate  an  electron  from  a 
fluorescing  molecule  than  from  a  non-fluorescing  molecule. 

There  are  a  number  of  processes  produced  by  light  which,  like 
fluorescence,  do  not  necessarily  involve  any  separation  of  electricity 
which  can  be  detected  by  our  methods.  Such  processes  are  the 
formation  of  ozone  from  oxygen  by  ultra-violet  light,  the  combina- 
tion of  hydrogen  and  chlorine  when  suitably  illuminated,  and  the 
decomposition  of  water  vapour  by  light. 

The  increased  conductivity  of  alcoholic  solutions  of  dyes  when 
illuminated  has  been  investigated  by  Goldmann1.  It  was  found  that 
there  was  no  increase  in  the  conductivity  itself,  but  that  an  electro- 
motive force  (about  '2  volt)  was  produced  in  a  capillary  layer  of 
the  dye  solution  bounded  by  an  electrode.  The  electromotive  force 
was  independent  of  the  light  intensity,  in  which  respect  it  behaves 
similarly  to  the  emission  velocities  of  photo-electrons.  The  light 
used  was  limited  to  the  visible  spectrum.  This  effect  is  probably 
similar  to  that  investigated  by  Volmer  for  the  longer  wave- 
lengths. 

Phosphorescent  Substances. 

Lenard  and  Saeland2  have  made  an  extensive  examination  of 
the  photo-electric  properties  of  a  certain  class  of  phosphorescent 

1  Goldman n,  Ann.  d.  Phy*.  xxvn.  p.  449,  1903. 

2  Lenard  and  Saeland,  Ann.  d.  Phys.  xxvin.  p.  476,  1909. 


128  PHOTO-ELECTRICITY  [CHAP. 

bodies.  These  substances,  which  were  previously  studied  by 
Lenard  and  Klatt1,  consist  of  a  sulphide  of  Ca,  Sr  or  Ba,  a  trace 
of  an  added  metal  such  as  Bi,  Ni  or  Pb,  and  a  flux  such  as  Na,S04 
or  Na2B407,  which  are  all  fused  together.  Such  a  substance,  called 
a  "phosphor,"  is  very  phosphorescent.  The  photo-electric  activity 
differs  very  much  between  different  "phosphors,"  and  even  the 
same  one  may  have  its  activity  altered  very  much  by  imperceptible 
surface  changes.  The  most  active  one,  calcium  sulphide,  with 
bismuth  as  the  added  metal,  gave  nearly  as  big  a  photo-electric 
effect  as  freshly  polished  magnesium.  The  maximum  emission 
velocity  did  not  exceed  that  corresponding  to  2  volts.  These  sub- 
stances are  good  insulators,  and  so  they  show  the  actino-dielectric 
effect  which  is  only  apparent  during  the  first  few  minutes  of 
illumination.  The  surface  charges  up  positively  until  no  further 
emission  of  photo-electrons  takes  place.  It  was  found  that  when 
the  surface  ceases  to  emit  any  more  electrons,  only  ^th  of  the 
surface  was  really  charged.  This  justifies  the  authors  in  con-j 
sidering  that  the  photo-electric  effect  is  not  distributed  over  the! 
surface,  but  is  localized  in  those  "  centres "  which  are  active  nr 
a  phosphorescent  sense.  Previous  investigations  had  led  Lenard 
to  associate  phosphorescence  with  active  "centres"  rather  than 
with  the  whole  mass  of  the  substance.  The  close  connection  between 
the  photo-electric  effect  and  the  phosphorescent  effect  was  estab- 
lished in  this  way.  Both  effects  were  tested  in 

(1)  pure  sulphide, 

(2)  added  metal, 

(3)  the  flux, 

and  in  combinations  of  these  two  by  two.  The  phosphorescence 
and  the  photo-electric  effect  were  only  well  marked  in  the  com- 
bination of  the  three  constituents. 

By  using  coloured  glasses  as  light  filters  it  was  established  that 
the  light  which  did  not  produce  phosphorescence  did  not  produce 
the  photo-electric  effect.  The  view  given  is  that  electrons  leave 
the  "centres"  and  become  embedded  in  the  surrounding  insulating 
medium.  The  phosphorescence  is  produced  by  the  electrons  falling 

1  Lenard  and  Klatt,  Ann.  d.  Phys.  xv.  p.  671,  1904. 


VIII]        FLUORESCENT  AND   PHOSPHORESCENT  SUBSTANCES  129 

back  into  the  polarised  centres.  The  duration  of  the  phosphor- 
escence is  determined  by  the  insulation  of  the  medium,  which  in 
turn  depends  on  the  temperature.  When  the  insulation  is  poor 
the  electrons  fall  into  the  polarised  "centres"  quickly  and  give 
a  short  duration  phosphorescence,  and  conversely.  When  the 
"  centres  "  are  on  the  surface  they  may  lose  some  of  their  electrons 
outwards,  giving  rise  to  a  photo-electric  effect.  The  nature  of  the 
phosphorescent  light  is  determined  by  the  disturbances  produced 
when  the  electrons  fall  into  the  "  centres,"  and  not  by  the  character 
of  the  exciting  light.  The  photo-electric  effect  ceases  immediately 
with  the  cutting  off  of  the  light,  and  hence  it  is  associated  with 
the  ejection  of  electrons  and  not  with  their  return  to  the  "centres." 
In  other  words,  the  photo-electric  effect  is  not  connected  with  the 
intensity  of  the  phosphorescence,  but  with  the  excitation  of  the 
phosphorescence. 

Butman1  finds  that  there  is  a  well-marked  photo-electric  effect 
in  the  CaBiNa  "  phosphor "  (i.e.  CaS  +  Bi  +  Na  flux),  and  that 
this  effect  requires  wave-lengths  less  than  \4100  to  produce  it. 
The  maximum  emission  velocity  does  not  exceed  that  corresponding 
to  '35  volt.  It  is  also  stated  that  sulphur  is  photo-electric  to 
wave-lengths  longer  than  X3200.  (This  is  not  in  agreement  with 
Goldmann  and  Kalandyk  s  results.)  Hence  Butman  concludes  that 
the  photo-electric  effect  of  the  "  phosphor  "  is  associated  with  that 
of  the  sulphur  in  it.  The  light  which  does  not  produce  phosphor- 
escence does  not  produce  the  photo-electric  effect.  This  statement 
does  not  appear  to  have  been  sufficiently  tested.  It  was  found 
that  the  light  from  an  arc  lamp  passed  through  red,  yellow  or  green 
glass  did  not  produce  either  effect.  To  establish  this  statement  on 
a  more  exact  basis  it  is  certainly  desirable  to  carry  out  the  tests 
using  narrow  bands  in  the  ultra-violet,  and  to  investigate  whether 
those  wave-lengths  which  are  particularly  active  in  stimulating 
phosphorescence  produce  a  big  photo-electric  effect. 

The  difference  between  fluorescence  and  phosphorescence 
appears  to  be  this.  In  phosphorescence,  the  electrons  get  away 
beyond  the  sphere  of  influence  of  the  "  centre,"  and  as  an  electron 
returns  to  a  polarised  "  centre  "  an  emission  of  light  occurs  whose 

1  Butman,  Phys.  Rev.   xxxiv.   pp.  158,  316,   1912;    Amer.  Jour.  Sci.   xxxiv. 
p.  133,  1912. 

H.  9 


130  PHOTO-ELECTRICITY  [CHAP.  VIII 

period  is  determined  by  the  disturbance  produced  as  the  electron 
settles  down  to  its  equilibrium  position  in  the  "  centre."  Hence, 
if  the  "centres"  lie  on  the  surface,  the  electron  may  get  away 
completely,  giving  a  photo-electric  effect.  '  In  fluorescence,  the 
electron  is  disturbed  but  does  not  get  away  beyond  the  sphere  of 
influence,  and  in  settling  down  to  its  equilibrium  position  the 
fluorescent  light  is  emitted. 

These  views  are  in  harmony  with  the  fact  that  a  photo-electric 
effect  accompanies  phosphorescence  but  does  not  as  a  rule  accom- 
pany fluorescence. 


CHAPTER  IX 

POSITIVE    RAYS    PRODUCED    BY   LIGHT 

NUMEROUS  as  are  the  difficulties  which  require  attention  in 
experiments  on  photo-electric  effects,  the  complication  arising  from 
the  emission  of  positively  charged  particles,  along  with  the  photo- 
electrons  from  an  illuminated  plate,  has  fortunately  never  been  a 
source  of  trouble.  It  has  been  tacitly  assumed  all  along  that  an 
illuminated  plate  does  not  emit  positive  electricity,  and  the  exist- 
ence of  a  positive  current  has  never  been  suggested,  directly  or 
indirectly,  by  experiments  on  other  aspects  of  photo-electricity. 
We  should,  however,  call  attention  to  the  interesting  experiments 
of  Dember1,  which  point  to  the  emission  of  a  very  feeble  current 
of  positive  rays  along  with  the  much  more  copious  stream  of 
electrons. 

The  apparatus  is  shown  in  Fig.  37.  A  is  a  thick  metal  plate 
which  is  perforated  near  the  centre  by  a  number  of  narrow  channels 
(£2:  1  mm.  diameter).  B  is  a  Faraday  cylinder  surrounding  the 
receiving  plate  G,  which  is  connected  to  an  electrometer.  D  is  a 
piece  of  gauze  which  serves  as  anode.  When  D  is  at  a  positive 
potential  relative  to  A,  the  photo-electrons  leaving  A  are  all  drawn 
into  the  gauze  and  the  current  is  measured  by  the  galvanometer  G. 
But  simultaneously  C  acquires  a  positive  charge  of  a  much  smaller 
order  of  magnitude.  The  positive  charge  can  arise  in  two  ways. 
The  electrons  leaving  A  and  accelerated  towards  D  produce  ions 
by  collision.  The  positive  ions  so  produced  will  be  directed  to- 
wards A  by  the  field,  and  some  of  them  will  go  through  the 
channels  and  yield  up  their  charges  to  C.  If  we  assume  that 
positive  particles  are  emitted  by  A  in  addition  to  photo-electrons, 

1  Dember,  Ann.  d.  Phys.  xxx.  p.  142,  1910. 

9—2 


132 


PHOTO-ELECTRICITY 


[CHAP. 


then  these  positive  particles  will  start  off  towards  D,  but  will  be 
forced  back  to  A  in  parabolic  paths  by  the  electric  field  and  some 
will  pass  through  the  channels.  These  two  effects  can  be  separated 
by  studying  the  way  in  which  the  current  varies  with  the  potential 
difference  between  A  and  D  at  different  pressures.  The  curve  in 
Fig.  38,  giving  the  positive  charge  acquired  by  G,  was  obtained 
when  the  residual  gas  was  at  a  pressure  of  "0008  mm.  It  is  quite 
evident  that  ionisation  of  the  gaseous  molecules  by  collision  sets 
in  when  the  potential  difference  becomes  greater  than  10  volts. 
On  reducing  the  distance  between  A  and  D  to  2  mm.,  and  the 
pressure  to  a  value  below  "00001  mm.,  the  curves  in  Fig.  39  were 
obtained.  The  Cu  and  Au  refer  to  the  illuminated  metal.  We 
see  that  the  current  is  nearly  constant  from  10  volts  to  40  volts;  so 


earth 


electrometer 


Fig.  37. 

evidently  no  positive  ions  are  produced  by  collision^  of  the  photo- 
electrons  with  gaseous  molecules  between  A  and  D.  It  might  be 
suggested  that  some  stray  light  finds  its  way  to  C  and  causes  it  to 
lose  electrons,  thereby  becoming  positively  charged.  But  changing 
the  field  between  A  and  D  from  0  volt  to  1  volt  and  to  40  volts 
should  have  no  effect  on  the  emission  of  electrons  from  C.  Dember 
therefore  concludes  that  positively  charged  particles  leave  the 
illuminated  surface  A  and  are  compelled  by  the  field  to  return 
towards  it,  some  of  them  penetrating  through  the  channels.  On 
this  view,  the  curves  in  Fig.  39  indicate  that  the  maximum  emis- 
sion energies  of  these  positive  particles  correspond  to  a  voltage 
of  from  4  to  6.  This  value  for  the  maximum  energy  appeared 


IX] 


POSITIVE   BAYS   PRODUCED   BY   LIGHT 


133 


to  remain  unchanged  as  the  light  intensity  increased  from  1  to 
1*8.  Using  a  zinc  plate  with  a  very  large  number  of  channels 
(68  holes  each  1  mm.  diameter),  the  positive  current  to  C  was 
3  x  10~13  amp.,  while  the  negative  current  to  D  was  3*7  x  lO"9  amp. 


12 


16  20 

Volts 


Fig.  38. 
Magnesium  *0008  mm.  air. 

This  very  large  ratio  of  the  negative  current  (photo-electrons)  to 
the  positive  current  probably  explains  why  the  positive  current 
does  not  interfere  with  the  usual  photo-electric  experiments. 

It  is  somewhat  strange  that  this  effect  has  not  been  investi- 
gated further  since  its  discovery  was  announced.  It  seems 
desirable  to  extend  the  investigation  in  various  directions  and  to 


300 


see  how  the  emission  of  the  positive  particles  depends  on  the 
different  factors,  such  as  the  frequency  and  intensity  of  the  light 
and  the  nature  of  the  illuminated  surface.  A  measurement  of 
the  ratio  e/m  for  the  positive  rays  from  different  metallic  surfaces 
should  tell  us  something  about  their  origin. 


CHAPTER  X 

SOURCES    OF   LIGHT    USED    IN    PHOTO-ELECTRIC 
EXPERIMENTS 

As  a  knowledge  of  the  wave-lengths  used  in  different  photo- 
electric experiments  is  of  great  importance  in  interpreting  the 
results,  it  will  be  useful  to  give  in  conclusion  a  short  account  of 
the  sources  of  light  most  generally  used  in  such  experiments. 

A.  The  most  useful  source  of  ultra-violet  light  for  general 
purposes  is  the  mercury  lamp,  a  convenient  form  of  which  is 


Fig.  40. 

shown  in  Fig.  40.  It  consists  of  a  tube  of  quartz  glass  (clear  fused 
silica)  about  1  cm.  in  diameter,  exhausted  as  completely  as  possible. 
Sufficient  mercury  is  put  into  the  tube  beforehand,  so  that  on 
tilting  it  an  electric  current  can  flow  from  A  to  B  through  liquid 
mercury.  On  bringing  the  lamp  back  again  to  its  normal  vertical 
position,  the  column  of  mercury  breaks  and  a  brilliant  arc  flashes 


CHAP.  X]     LIGHT  USED   IN   PHOTO-ELECTRIC  EXPERIMENTS  135 

out  between  C  and  D.  Copper  radiators  are  generally  fixed  out- 
side the  quartz  tube  to  convey  the  heat  away  from  the  electrodes, 
and  so  the  lamp  is  kept  comparatively  cool.  The  electric  current 
through  the  lamp  is  at  first  large,  but  after  10  or  20  minutes  it 
drops  to  its  final  value  and  then  the  emission  of  light  becomes 
remarkably  constant.  The  constancy  of  the  emission  of  light,  its 
great  intensity,  and  the  fact  that  the  lamp  once  started  needs  no 
attention  whatever,  account  for  the  popularity  of  the  lamp  as  a 
source  of  ultra-violet  light.  The  voltage  generally  used  for  mer- 
cury lamps  is  between  50  and  200  volts  and  the  current  is  from 
3  to  5  amperes.  The  ultra-violet  light  from  the  mercury  lamp 
and  other  powerful  sources  produces  painful  effects  in  the  eyes 
when  they  are  exposed  to  it  for  any  length  of  time.  It  is  therefore 
advisable  to  enclose  the  lamp  in  a  box  so  arranged  that  the  light 
can  be  transmitted  only  into  the  photo-electric  apparatus.  The 
spectrum  of  the  mercury  arc  in  vacuo  consists  of  a  large  number 
of  bright  lines  extending  from  about  X2300  to  X5790.  A  useful 
list  of  the  more  intense  lines  is  given  by  Arons1.  The  line  X2540 
is  particularly  effective  in  producing  photo-electrons  from  most 
metals,  because  of  its  great  intensity  and  its  situation  well  in  the 
ultra-violet.  A  number  of  very  weak  lines  are  found  below  X2000, 
the  shortest  being  XI 849.  These  lines  do  not  show  up  readily  in 
photographs  of  the  spectrum  of  the  mercury  arc.  Nevertheless, 
they  are  of  great  importance  in  experiments  on  emission  velocities 
of  photo-electrons  (Chapter  in).  The  mercury  arc  itself  emits 
light  of  still  shorter  wave-length,  which  however  is  absorbed  by 
the  quartz  glass  of  the  lamp. 

B.  Electric  sparks,  produced  by  an  induction  coil  between 
various  metallic  terminals,  with  a  condenser  in  parallel,  are  fre- 
quently used  as  sources  of  ultra-violet  light.  Their  disadvantage 
lies  in  the  fact  that  it  is  extremely  difficult  to  keep  them  steady. 
On  the  other  hand,  they  emit  light  of  shorter  wave-lengths  and 
of  greater  intensity  than  the  mercury  lamp.  The  spark  between 
aluminium  terminals  gives  very  powerful  lines  at  X1852,  X1864, 
XI 935,  and  XI 990.  Still  shorter  wave-lengths  are  recorded  by 
Morris  Airy2  at  X1785,  X1741,  X1709,  and  X1693,  and  also  by 

1  Arons,  Ann.  d.  Phys.  xxm.  p.  176,  1905. 

2  Morris  Airy,  Manchester  Lit.  and  Phil  Soc.  XLIX.  p.  1,  1905. 


136  PHOTO-ELECTRICITY  [CHAP. 

Lyman1.  Lenard2  has  described  a  source  of  ultra-violet  light  of 
very  great  power.  A  short  spark  between  aluminium  terminals 
is  produced  by  a  big  induction  coil,  the  primary  of  which  takes 
90  amperes.  The  condenser  in  parallel  with  the  spark  has  a 
capacity  of  '11  microfarad.  The  rate  at  which  energy  is  given 
out  by  such  a  spark  exceeds  1000  watts,  which  is  greater  than  the 
power  of  many  carbon  arcs.  Such  a  source  is  very  rich  indeed  in 
light  of  short  wave-lengths.  Lyman3  gives  a  list  of  wave-lengths 
down  to  XI 239  for  the  light  emitted  by  a  bright  aluminium 
spark,  which  however  was  much  less  intense  than  Lenard's 
spark. 

C.  The  discharge  in  hydrogen  at  a  pressure  of  1  to  5  min. 
is  extremely  rich  in  light  of  very  short  wave-length.     A  large 
number  of  lines  between  X1030  and  X1650  has  been  recorded  by 
Lyman4.     Such  a  discharge  is  very  feeble  to  the  eye  compared 
with    the   intense   light   from  a  mercury  lamp.     Yet   Hull   and 
St  John5  found  that  the  light  from  such  a  discharge  in  hydrogen, 
when  passed  through  a  fluorite  plate,  produced  a  photo-electric 
effect  at  a  zinc  plate  250  times  greater  than  that  produced  by  a 
mercury  lamp.    The  reason  for  this  is  that  the  hydrogen  discharge 
emits  far  more  energy  in  the  extreme  ultra-violet  than  does  the 
mercury  lamp. 

D.  The  ordinary  carbon  arc  has  occasionally  been  used  as  a 
source  of  ultra-violet   light.     The   intensity  of  the    ultra-violet 
spectrum  falls  off  rapidly,  being  inappreciable  beyond  X2400. 

Transparency  Limits  of  different  Substances. 

The  source  of  light  has  in  most  cases  to  be  separated  from  the 
experimental  chamber  by  some  air-tight  transparent  window,  and 
its  transparency  limit  (that  is,  the  shortest  wave-length  which  it 
transmits)  should  be  known  in  addition  to  the  spectral  range  of 
the  source.  Lyman's  investigations6  of  the  transparencies  of 

' l  Lyman,  Astrophysical  Journal,  xxxv.  p.  341,  1912. 

2  Lenard,  Sitzungsberichte  d.  Held.  AJcad.  d.  Wlssen.  1910. 

3  Lyman,  Astrophysical  Journal,  xxxv.  p.  341,  1912. 

4  Lyman,  Astrophysical  Journal,  xxm.  p.  181,  1906. 
6  Hull  and  St  John,  Phys.  Rev.  (2),  i.  p?  329,  1913. 
6  Lyman,  Astrophysical  Journal,  xxv.  p.  45,  1907. 


X]  LIGHT  USED   IN   PHOTO-ELECTRIC   EXPERIMENTS  137 

various  substances  are  most  useful  for  our  purpose.  Clear  colour- 
less fiuorite  is  the  most  transparent  substance  known.  The  best 
specimens  (1  to  2  mm.  thick)  transmit  as  far  as  XI 250. 

Plates  of  crystalline  quartz,  in  thickness  of  about  *2  mm., 
transmit  to  X1450,  of  2  mm.  to  X1500,  and  of  20  mm.  to  X1600. 
Rock  salt  (2  mm.  thick)  is  less  transparent,  the  limit  being  XI 7  70. 
The  author  tested  the  transparency  of  clear  quartz  glass  (or  fused 
silica).  The  plate,  which  was  '3  or  *4  mm.  thick,  transmitted 
24%  of  X1849,  36°/o  of  X1971,  and  40%  of  X2002.  The  very 
rapid  increase  in  opacity  explains  why  XI 8 49  is  the  shortest  wave- 
length emitted  by  an  ordinary  mercury  lamp  made  of  quartz  glass. 
Common  soda  glass,  2  or  3  mm.  thick,  transmits  to  about  X3300. 
When  considerably  thinner,  say  '2  mm.  or  less,  it  may  easily  trans- 
mit as  far  as  X2500.  Mica,  even  in  the  thinnest  sheets,  has  sharply 
defined  transparency  limits,  which  vary  a  little  with  the  specimen 
of  mica  but  are  usually  near  to  X3000. 

A  column  of  water  1  cm.  long  cuts  out  all  wave-lengths  shorter 
than  X2200. 

Many  of  the  common  gases  absorb  strongly  in  the  extreme 
ultra-violet,  frequently  termed  the  Schumann  region.  We  are 
indebted  to  Lyman1  for  exact  information  about  the  absorption  of 
gases  in  this  region.  The  gases  were  all  tested  in  a  cell  '91  cm. 
long.  Hydrogen  is  quite  transparent.  Nitrogen  (760  mm.)  shows 
only  a  very  slight  absorption,  which  increases  regularly  with  de- 
creasing wave-length,  though  even  at  XI 250  the  absorption  is  very 
small.  Oxygen  has  an  absorption  band  which  broadens  unsym- 
metrically  with  increasing  pressure.  At  atmospheric  pressure  it 
extends  from  X1270  to  X1760,  at  40  mm.  from  X1330  to  X1600, 
and  at  15  mm.  from  XI 350  to  XI 500.  Carbon  monoxide  has  eight 
narrow  absorption  bands  between  XI 250  and  XI 600.  Carbon 
dioxide  has  a  broad  band  like  that  of  oxygen,  the  position  of  the 
more  refrangible  end  being  unknown.  The  absorption  of  air  is 
similar  to  that  of  oxygen,  though  under  like  conditions  the  air 
band  is  slightly  narrower  than  the  oxygen  band. 

I  have  investigated  the  short  wave-length  limit  of  a  number  of 
quartz  and  fluorite  plates,  using  the  maximum  emission  velocities 
of  photo-electrons  as  an  indication  of  the  shortest  wave-length 
1  Lyman,  Astrophysical  Journal,  xxvu.  p.  87,  1908. 


138  PHOTO-ELECTRICITY  [CHAP. 

transmitted.  There  was  little  or  no  variation  in  the  transparency 
of  the  quartz  plates  (approximately  *3  mm.  thick),  but  the  varia- 
tions in  the  transparency  of  clear  colourless  fluorite  were  extra- 
ordinary. Out  of  thirty  or  more  specimens,  not  more  than  five 
transmitted  further  than  quartz,  and  many  of  the  others  were 
considerably  worse  than  quartz.  Two  specimens  (from  different 
sources)  of  perfectly  clear  colourless  fluorite  supplied  by  Zeiss  had 
approximately  X1330  and  XI 700  as  their  respective  limits.  Hence 
it  is  unjustifiable  to  assume  that  the  transparency  of  fluorite  is 
the  same  as  that  of  Lyman's  best  specimens.  Each  piece  should 
be  tested  separately,  and  it  is  not  easy  to  do  this  spectroscopically 
as  the  vacuum  spectroscope  which  is  necessary  is  not  usually 
available.  It  seems,  however,  that  we  can  rely  on  plates  of  quartz 
*2  or  '3  mm.  thick  transmitting  down  to  X1450,  and  plates  2  mm. 
thick  transmitting  to  XI 500.  Lenard1  assigns  to  crystalline  quartz 
a  transparency  limit  X1800  and  to  quartz  glass  X2200.  In  view 
of  Lyman's  direct  measurements  on  crystalline  quartz,  this  seems 
doubtful ;  it  is  well  to  remember  this  when  considering  Lenard's 
experiments.  I  have  obtained  XI 849  from  mercury  lamps  of 
quartz  glass,  the  thickness  of  the  tube  being  about  '5  to  1  mm. 
It  should  be  remembered  that  in  photo-electric  experiments  the 
effects  produced  increase  very  rapidly  with  decreasing  wave- 
lengths, and  wave-lengths  which  are  too  weak  to  give  any  photo- 
graphic record  spectroscopically  without  special  precautions  may 
play  the  most  important  part  in  a  photo-electric  experiment. 
For  example,  anthracene,  when  illuminated  by  the  light  from  a 
mercury  lamp,  is  photo-electrically  active,  and  direct  measure- 
ments show  that  only  light  of  wave-length  shorter  than  X2200 
is  effective.  But  lines  of  shorter  wave-length  than  this  do  not 
appear  on  the  photographs  of  the  mercury  arc  spectrum  unless 
long  exposures  are  given. 

On  considering  the  above  data,  we  arrive  at  the  following 
conclusions.  The  shortest  wave-length  emitted  by  the  ordinary 
mercury  lamp  is  XI 849.  The  shortest  wave-length  emitted  by  a 
hydrogen  discharge  through  a  fluorite  window  may  be  XI 250  if 
the  fluorite  is  of  the  best  quality.  The  fluorite  should  be  tested 
for  transparency.  If  a  thin  quartz  window  (<  '5  mm.  thick)  be 

1  Lenard,  Sitzttngsberichte  d.  Held.  Akad.  d.  Wissen.  p.  35,  November,  1910. 


X]  LIGHT  USED   IN   PHOTO-ELECTRIC   EXPERIMENTS  139 

used  instead,  the  limit  may  be  assumed  to  be  XI 450.  Should  the 
light  be  then  transmitted  through  a  centimetre  of  oxygen  or  air, 
the  limits  are  shifted  to  X1770  and  X1710  respectively.  If,  in- 
stead of  quartz,  fluorite  is  used  with  the  oxygen  column,  a  narrow 
band  would  be  emitted  between  XI 250  and  XI 2 70,  in  addition  to 
the  wave-lengths  longer  than  XI 7 70,  if  the  fluorite  is  of  the  best 
quality.  Very  little  is  known  of  the  emission  from  sparks  in  the 
short  wave-length  region,  but  assuming  that  no  wide  gaps  exist  in 
the  emission  spectra,  then  the  shortest  wave-length  is  determined 
approximately  by  the  transparency  limits  of  the  fluorite,  quartz, 
air,  or  other  medium  through  which  the  light  passes.  Lyman1 
gives  a  list  of  a  number  of  aluminium  spark  lines  below  XI 700. 
The  aluminium  spark  in  air  emits  a  group  of  strong  lines  near 
XI 300,  and  these  are  very  effective  in  ionising  air. 


Light  Filters. 

To  isolate  any  required  region  of  the  spectrum,  a  mono- 
chromator  is  most  useful.  The  instruments  now  available  are 
not  designed  to  isolate  wave-lengths  shorter  than  XI 849.  Light 
filters  can  often  be  used  instead  of  a  monochromator  with  advan- 
tage, but  their  use  is  limited  to  wave-lengths  longer  than  X3000, 
as  no  substance  is  known  to  exhibit  a  selective  transmission 
beyond  this  wave-length.  Lasts  of  light  filters  are  given  in  R.  W. 
Wood's  Physical  Optics,  in  a  paper  by  Luther  and  Forbes2,  and  in 
other  papers.  I  have  found  the  following  filters  useful  in  isolating 
the  mercury  lines : 

X5790   and   X5770.      Wratten   and   Wainwright's    yellow    filter, 

No.  22. 

X5461.     Wratten  and  Wainwright's  green  filter,  No.  62. 
X4360.     Separate  solutions  of  potassium  permanganate  and  nickel 

nitrate,  of  just  sufficient  concentration  to  cut  out  other  lines. 
X3650.     Nitrosodimethylaniline  and  methyl  violet  transmit  X3650 

and  X3340.    The  X3340  was  cut  out  by  a  thick  block  of  glass. 

1  Lyman,  Astrophysical  Journal,  xxxv.  p.  341,  1912. 

2  Luther  and  Forbes,  J&ur.  Chem.  Soc.  xxxi.  p.  770,  1909. 


140  PHOTO-ELECTRICITY  [CHAP.  X 

X3130.  K  W.  Wood  recommends  a  silver  film  deposited  on 
quartz.  Unless  the  film  is  so  thick  as  to  reduce  the  intensity 
of  X3130  very  considerably,  many  of  the  other  lines  appear  as 
well.  I  found  that  a  certain  sheet  of  white  mica  transmitted 
X3130  almost  entirely,  and  was  opaque  to  X3027  and  shorter 
wave-lengths.  Thus  we  can  get  a  sharp  limit  on  the  ultra- 
violet side  of  X3130.  This  may  be  useful  in  cases  when  the 
presence  of  other  lines  longer  than  X3130  makes  but  little 
difference. 

Winther1  gives  a  list  of  ultra-violet  filters,  which  are  said  to 
transmit  from  30%  to  40°/0  of  the  selected  lines.  These  filters 
should  be  very  useful  provided  that  the  intensity  of  the  light  of 
other  wave-lengths  is  reduced  to  such  an  extent  that  its  effects 
are  negligible. 

1  Winther,  Zeits.f.  Elektrochem.  xix.  p.  389,  1913. 


NAME  INDEX 


Allen  70-74 
Anderson  25 
Arons  135 

Badeker  114 
von  Baeyer  36 
Beatty  92 
Becker  72 
Bergwitz  73 
van  der  Bijl  34 
Borck  123 
Braun  79 
Brillouin  114 
Butman  129 
Byk  123 

Cannegieter  17 
Compton  30,  32,  37,  41 
Cornelius  37 

Dember  65,  73,  131-133 
Dike  97 
Duncan  88 

Einstein  43 

Elster  28,  59,  64,  65,  68,  69,  78 

Forbes  139 
Franck  21 


Gehrts  36 

Geitel  28,  59,  64,  65,  66 
Goldmann  102-107,  127 
Griffith  59 


),  78 


Hallwachs  70-74,  79,  94,  109,  119 

Harms  64 

Henry  21 

Herrmann  50,  74,  75,  111 

Hertz  21 

Hughes  12,  24,  37,  102,  109,  111,  114, 

117,  124 
Hull  136 


Jaffe"  117 
Joffe  35 

Kalandyk  102-107 
Kemp  69 
Klages  36 
Klatt  127 
Kleeman  93 
Knoblauch  111 
Kunz  37,  42 

Ladenburg  28,  30,  35,  42,  66,  73,  77, 

78 
Lenard   3,  9,    17-19,  48,   55,  59,  127, 

134,  137 
Lichtenecker  61 
Lienhop  42 
Liiidemann  69,  88 
Lorentz  63 
Luther  139 
Lyman  13,  15,  136-139 

Marx  61 

Merritt  64 

Millikan  28,  29,  36,  37,  42,  66,  73 

Mohlin  28,  77 

Morris  Airy  135 

Nichols  64 
Obolensky  115 

Palmer  15 

Partzsch  57,  94 

Pochettino  111,  123 

Pohl  29,  60,  69,  75,  79,  81-87,  90 

Pringsheim  29,  60,  69,  75,  81-87,  90 

Kamsauer  17-19 

Ramsey  111 

Beboul  111 

Eeiger  117 

Richardson  30,  32,  44,  45,  96 


142 


NAME   INDEX 


Eichtmyer  64,  73 
Eies  107 
Bohde  110,  119 

Saeland  127 
St  John  136 
Schaffer  117 
Schmidt  111,  119 
Scholl  113 
v.  Schweidler  55 
Serkof  24 
Spencer  111 
Stark  22,  121,  126 
Steubing  25,  121 
Stoletow  55,  119 
Stuhlmann  93 
Swann  97 
Szivessy  117 


Thomson,  Sir  J.  J.  3,  11,  50,  56,  65 
Townsend  56 

Ullmann  71,  72 
Unwin  65 

Varley  54,  65 
Volmer  117,  124 

Westphal  21 
Whiddington  21 
Wilson,  C.  T.  K.  7,  10 
Wilson,  W.  109,  113 
Winchester  28,  36,  42,  66,  73 
Winther  140 

Zeleny  65 


SUBJECT  INDEX 


Actino-dielectric  effect  108,  122,  128 
Alkali  metals,  photo-electric  properties  of  77-87 
Alloys,  photo-electric  effect  of  75-76,  84-85 
Atomic  volume,  relation  of  ionising  potential  to  51 

Colloidal  modification  of  alkali  metals  68-69 

photo-electric  sensitiveness  of  87 
Condensation  nuclei 

method  of  investigating  ionisation  10-11 

produced  by  light  19 
Conduction  produced  by  illumination 

in  sulphur  103-107 
silver  iodide  113-114 
solutions  124-126 
Contact  potential  32,  42 
Corpuscular  pressure  100-101 

Decomposition  of  salts  by  ultra-violet  light  111-112 
Electric  discharge  and  photo-electric  sensitiveness  36,  66-68 

Fatigue,  photo-electric  70-75 

Fluorescent  substances,  photo-electric  effect  of  119-127 

Fluorite,  transparency  of  137-139 

Fluorite-violet  17 

Gases,  effect  of,  on  the  photo-electric  effect  of  metals  53-58 
Gases,  ionisation  in  7-21 

Hydrides,  photo-electric  effect  of  certain  68 

Intensity  of  light  and  the  photo-electric  current  58-64 
Intensity  of  light  and  the  velocities  of  photo-electrons  28-29 
Intermittent  light,  photo-electric  effect  with  61 
louisation  in  gases  and  vapours  by  ultra-violet  light  7-26 
Ionising  potential  51,  108 

experimental  values  20,  40,  58 

Light  niters  139 

Liquids,  photo-electric  effect  of  114-117 

Long  wave-length  limit  of  the  actino-dielectric  effect  107-108 
Long  wave-length  limit  of  the  photo-electric  effect  4-5,  51,  100 
for  air  16,  19-21 

alloys  75-76,  84-85 

anthracene  124 

metals  40-41 

Mercury  arc  as  a  source  of  ultra-violet  light  134-135 

Metallic  vapours,  ionisation  of  25 

Mobility  of  ions  produced  by  ultra-violet  light  13,   18 

Normal  effect  82-87 


144  SUBJECT   INDEX 

Organic  substances,  photo-electric  effects  of  119-127 
Organic  vapours,  ionisation  by  ultra-violet  light  of  22-24 

Phosphorescent  substances,  photo-electric  effect  of  127-130 
Photo-electric  cells  64,  68-69 
Photo-electric  effect  of 

metals  35-42,  53-99 

non-metallic  elements  100-108 

inorganic  compounds  109-117 

organic  compounds  119-124 

insulators  101-102,  117 

Polarised  light,  photo-electric  effect  with  77-89 
Positive  rays  produced  by  light  131-133 

Quantum  theory  5,  20,  42,  63 
Quartz,  transparency  of  137-139 
Quartz-violet  17 

Kadiometry,  applications  of  the  photo-electric  effect  to  64 
Eesonance,  photo-electric  effect  regarded  as  47-51,  61-64 

Schumann  region  11,  137 
Selective  effect  82-89 

velocities  of  photo-electrons  in  78,  88 
Sensitiveness,  photo-electric 

in  the  infra-red  69,  90 

of  alkali  metals  82-89 

of  newly  formed  surfaces  89-91 

Sodium-potassium  alloy,  photo-electric  properties  of  81 
Solutions,  photo-electric  effect  of  116 
Spark,  electric,  as  a  source  of  ultra-violet  light  135-136 
Statistical  theory  of  the  photo-electric  effect  45 

Temperature 

relation  of  photo-electric  effect  to  65-66 

relation  of  velocities  of  photo-electrons  to  42 
Thin  films,  photo-electric  properties  of  92-99 
Transparency  for  ultra-violet  light  of 

air  137 

hydrogen  137 

oxygen  15,  137 

quartz  137-139 

fluorite  137-139 

mica  137 

water  137 

Velocities  of  photo-electrons  27-52 
distribution  of  velocities  31-34 
measurement  of  27-28,  31-34 
relation  to  intensity  of  light  28-29 
relation  to  frequency  29-42 
relation  to  nature  of  metal  40-41 


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